MathDB

6

Part of 1989 IMO Shortlist

Problems(1)

16Q^3 >= 27r^4P

Source: IMO Shortlist 1989, Problem 6, ILL 14

9/18/2008
For a triangle ABC, ABC, let k k be its circumcircle with radius r. r. The bisectors of the inner angles A,B, A, B, and C C of the triangle intersect respectively the circle k k again at points A′,B′, A', B', and C′. C'. Prove the inequality
16Q3≥27r4P, 16Q^3 \geq 27 r^4 P,
where Q Q and P P are the areas of the triangles A′B′C′ A'B'C' and ABCABC respectively.
geometrycircumcirclegeometric inequalityarea of a triangleIMO Shortlist