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prove that L_1 and L_2 are equidistant from line AB

Source: Sharygin Geometry Olympiad 2014 Correspondence Round P12

August 1, 2018

geometrycircumcirclecircles

Problem Statement

Circles

\omega_1

and

\omega_2

meet at points

A

and

B

. Let points

K_1

and

K_2

of

\omega_1

and

\omega_2

respectively be such that

K_1A

touches

\omega_2

, and

K_2A

touches

\omega_1

. The circumcircle of triangle

K_1BK_2

meets lines

AK_1

and

AK_2

for the second time at points

L_1

and

L_2

respectively. Prove that

L_1

and

L_2

are equidistant from line

AB

.

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