Các bổ đề Hình học THCS

I. CÁC BỔ ĐỀ VỚI CÁC YẾU TỐ ĐẶC BIỆT CỦA TAM GIÁC: 1.            0  0 . 2. Cho  DEF. ,  có chu ).      . 3.   D E F H B C A 4.                                   4.2.              4.3.    5.   B, C.                               N M D E F H B C A 6.       7.  .         8.   g. N M D E B C A Q P 10.                                  Cho tam gi    là bán kính các .            .                                           II. CÁC BỔ ĐỀ VỀ TỨ GIÁC: 1.   hàng). 2.   3.   4.    5.   6.    7.   () 8.   8.1.                   các góc      8.2.        quy   8.3.  PN    8.4.   AC là phân giác góc      iác góc    BD là phân giác góc   . 8.5.      III. CÁC BỔ ĐỀ VỀ ĐƯỜNG TRÒN 1.                 2.  2.1.     . 2.2.     3. :               }       A, B thì          4.                      5.    a  (O). 6.   M  7. Cho                                       .                8.           ABOC là hình vuông        .                   N       BC. 9.   à               .   a.  b.  c.              10.             . Cho 

I. CÁC BỔ ĐỀ VỚI CÁC YẾU TỐ ĐẶC BIỆT CỦA TAM GIÁC: 1.            0  0 . 2. Cho  DEF. ,  có chu ).      . 3.   D E F H B C A 4.                                   4.2.              4.3.    5.   B, C.                               N M D E F H B C A 6.       7.  .         8.   g. N M D E B C A Q P 10.                                  Cho tam gi    là bán kính các .            .                                           II. CÁC BỔ ĐỀ VỀ TỨ GIÁC: 1.   hàng). 2.   3.   4.    5.   6.    7.   () 8.   8.1.                   các góc      8.2.        quy   8.3.  PN    8.4.   AC là phân giác góc      iác góc    BD là phân giác góc   . 8.5.      III. CÁC BỔ ĐỀ VỀ ĐƯỜNG TRÒN 1.                 2.  2.1.     . 2.2.     3. :    /           }       A, B thì          4.                      5.    a  (O). 6.   M  7. Cho                                   //   //   .                8.           ABOC là hình vuông        .                   N       BC. 9.   à               .   a.  b.  c.              10.             [...]... giác lồi ABCD nội tiếp (O) có đường chéo AC cố định có chu vi và ̂ diện tích lớn nhất  B, D là các điểm chính giữa 2 cung AC  Trong các tam giác nội tiếp (O), tam giác đều có chu vi và diện tích lớn nhất  Trong các tứ giác lồi nội tiếp (O), hình vuông có chu vi và diện tích lớn nhất 13 Cho tam giác ABC đều nội tiếp (O R) M  MB MC ̂ BC, AM cắt BC tại D MA  14 Tổng quát hơn: ̂  Cho tam giác ABC... thì: a) MB MC MA 1 1 1 b) MB MC MD 15 Các cung đặc biệt và độ dài dây tính theo R: ố đo cung ̂ 1 0 1 0 120 0 60 30 16 Đường tròn nội tiếp: Độ dài dây BC BC 2R R(√6 √2 ) BC 2 BC R√3 BC R√2 BC R R(√6 √2 ) BC 2 16.1 Tứ giác ABCD ngoại tiếp (O)  AB CD AD BC 16.2 Cho tam giác ABC nội tiếp (O R) và có đường tròn nội tiếp (I r) Gọi M, N, P lần ̂ ̂ ̂ lượt là điểm chính giữa các cung BC, CA, AB Ta có:    ...11 Cho tam giác ABC nội tiếp (O) M là điểm bất kì trên (O) (M không trùng A, B, C) Gọi H, I, K lần lượt là hình chiếu của M lên BC, CA, AB M , M , M lần lượt đối xứng với M qua AB, BC, CA L là trực tâm tam giác ABC  H, I, K thẳng hàng (đường thẳng impson)  M , M , M , L thẳng hàng (đường thẳng Steiner) 12... BC 16.2 Cho tam giác ABC nội tiếp (O R) và có đường tròn nội tiếp (I r) Gọi M, N, P lần ̂ ̂ ̂ lượt là điểm chính giữa các cung BC, CA, AB Ta có:     M là tâm đường tròn ngoại tiếp tam giác BIC Tâm các đường tròn ngoại tiếp (AIB), (BIC), (CIA) thuộc (O) OI √R(R 2r) R 2r . Cho  DEF. ,  có chu )           ABOC là hình vuông        .