MathDB

5

Part of 2008 Dutch IMO TST

Problems(1)

midpoint of CQ lies on \Gamma, right triangle and semicircle related

Source:

8/4/2019
Let △ABC\vartriangle ABC be a right triangle with ∠B=90o\angle B = 90^o and ∣AB∣>∣BC∣|AB| > |BC|, and let Γ\Gamma be the semicircle with diameter ABAB that lies on the same side as CC. Let PP be a point on Γ\Gamma such that ∣BP∣=∣BC∣|BP| = |BC| and let QQ be on ABAB such that ∣AP∣=∣AQ∣|AP| = |AQ|. Prove that the midpoint of CQCQ lies on Γ\Gamma.
geometrysemicirclemidpoint