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equal segments in a triangle, angle chasing (Greece Junior 2001)

Source:

July 12, 2019

geometryequal segmentsAngle Chasing

Problem Statement

Let

ABC

be a triangle with altitude

AD

, angle bisectors

AE

and

BZ

that intersecting at point

I

. From point

I

let

IT

be a perpendicular on

AC

. Also let line

(e)

be perpendicular on

AC

at point

A

. Extension of

ET

intersects line

(e)

at point

K

. Prove that

AK=AD

.

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