MathDB

Humpty config

Source: Russian TST 2016, Day 10 P1 (Group B)

April 19, 2023

geometry

Problem Statement

The circles

\omega_1

and

\omega_2

intersect at

K{}

and

L{}

. The line

\ell

touches the circles

\omega_1

and

\omega_2

at the points

X{}

and

Y{}

, respectively. The point

K{}

lies inside the triangle

XYL

. The line

XK

intersects

\omega_2

a second time at the point

Z{}

. Prove that

LY

is the bisector of the angle

XLZ

.

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