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CK _|_ A'B' wanted, <BAC =60^o

Source: 2022 Oral Moscow Geometry Olympiad grades 8-9 p4

April 17, 2022

perpendicularityperpendiculargeometry

Problem Statement

In triangle

ABC

, angle

C

is equal to

60^o

. Bisectors

AA'

and

BB'

intersect at point

I

. Point

K

is symmetric to

I

with respect to line

AB

. Prove that lines

CK

and

A'B'

are perpendicular.
(D. Shvetsov, A. Zaslavsky)