... s iss4− 2(2R2+ 10Rr − r2)s2+ r(4R + r)2≤ 0.Exercise 26. With the usual notation for a triangle, show that 4R + r ≥√3s.16Exercise 27. ([WJB2],[RAS], W. J. Blundon) Let R and r denote ... (3√3 − 4)r.Exercise 28. Let G and I be the centroid and incenter of the triangle ABC with inradius r, semiperimeters, circumradius R. Show thatGI2=19s2+ 5r2− 16Rr.17Exercise 29. ... where z ≥ x, y.Exercise 20. Let f(x, y) be a real polynomial such that, for all θ ∈ R3,f(cos θ, sin θ) = 0.Show that the polynomial f(x, y) is divisible by x2+ y2− 1.Exercise 21. Let...