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[ABC] = 1/2 [AC'BA'C B'$] convex , <A+<B+<C =<A' +<B'+<C'

Source: TOT 532 1997 Spring J A4 - - Tournament Of Towns

September 11, 2024
geometryangleshexagonareas

Problem Statement

AC′BA′CB′AC' BA'C B' is a convex hexagon such that AB′=AC′AB' = AC', BC′=BA′BC' = BA', CA′=CB′CA' = CB' and ∠A+∠B+∠C=∠A′+∠B′+∠C′\angle A +\angle B + \angle C = \angle A' + \angle B' + \angle C'. Prove that the area of the triangle ABCABC is half the area of the hexagon.
(V Proizvolov)
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