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Wait! T is the Dumpty point!

Source: Sgarygin CR P11(Grades 8-10)

March 4, 2022

Sharygin Geometry OlympiadSharygin 2022geometry

Problem Statement

Let

ABC

be a triangle with

\angle A=60^o

and

T

be a point such that

\angle ATB=\angle BTC=\angle ATC

. A circle passing through

B,C

and

T

meets

AB

and

AC

for the second time at points

K

and

L

.Prove that the distances from

K

and

L

to

AT

are equal.

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