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A disrespectfully easy geo

Source: Bulgaria EGMO TST 2016 Day 1 Problem 2

February 3, 2023

geometrysimilar trianglesright trianglecircumcircle

Problem Statement

Let

ABC

be a right triangle with

\angle ACB = 90^{\circ}

and centroid

G

. The circumcircle

k_1

of triangle

AGC

and the circumcircle

k_2

of triangle

BGC

intersect

AB

at

P

and

Q

, respectively. The perpendiculars from

P

and

Q

respectively to

AC

and

BC

intersect

k_1

and

k_2

at

X

and

Y

. Determine the value of

\frac{CX \cdot CY}{AB^2}

.

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