MathDB

2007.11

Part of Ukraine Correspondence MO - geometry

Problems(1)

AQ/AP wanted, 2 circumcircles each passing through a midpoint

Source: 2007 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-11 p11

4/28/2021
Denote by B1B_1 and C1C_1, the midpoints of the sides ABAB and ACAC of the triangle ABCABC. Let the circles circumscribed around the triangles ABC1ABC_1 and AB1CAB_1C intersect at points AA and PP, and let the line APAP intersect the circle circumscribed around the triangle ABCABC at points AA and QQ. Find the ratio AQAP\frac{AQ}{AP}.
ratiogeometrycircumcircleUkraine Correspondence