MathDB

2017 Team #10: Line passes through fixed point

Source:

February 19, 2017

geometry

Problem Statement

Let

LBC

be a fixed triangle with

LB = LC

, and let

A

be a variable point on arc

LB

of its circumcircle. Let

I

be the incenter of

\triangle ABC

and

\overline{AK}

the altitude from

A

. The circumcircle of

\triangle IKL

intersects lines

KA

and

BC

again at

T

and

V \neq K

. Finally, let

T

be the projection of

I

onto line

UV

. Prove that the line through

T

and the midpoint of

\overline{IK}

passes through a fixed point as

A

varies.

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