MathDB

Rioplatense 2022 - Level 2 - Problem 3

Source:

December 6, 2022

geometry

Problem Statement

Let

ABC

be a triangle with

AB<AC

. There are two points

X

and

Y

on the angle bisector of

B\widehat AC

such that

X

is between

A

and

Y

and

BX

is parallel to

CY

. Let

Z

be the reflection of

X

with respect to

BC

. Line

YZ

cuts line

BC

at point

P

. If line

BY

cuts line

CX

at point

K

, prove that

KA=KP

.

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