MathDB

Line passing through vertex of rhombus tangent to circle

Source: St Petersburg 2021 10.6

December 23, 2021

geometryrhombuscircumcircle

Problem Statement

A line

\ell

passes through vertex

C

of the rhombus

ABCD

and meets the extensions of

AB, AD

at points

X,Y

. Lines

DX, BY

meet

(AXY)

for the second time at

P,Q

. Prove that the circumcircle of

\triangle PCQ

is tangent to

\ell

A. Kuznetsov