MathDB

3

Part of 2021 Canadian Mathematical Olympiad Qualification

Problems(1)

Circles centred at vertices of regular pentagon

Source: Canada Repêchage 2021/3 CMOQR

3/30/2021
ABCDEABCDE is a regular pentagon. Two circles C1C_1 and C2C_2 are drawn through BB with centers AA and CC respectively. Let the other intersection of C1C_1 and C2C_2 be PP. The circle with center PP which passes through EE and DD intersects C2C_2 at XX and AEAE at YY. Prove that AX=AYAX = AY.
Canadarepechagegeometrypentagon