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Croatian mathematical olympiad, day 2 problem 3

Source:

April 10, 2011

geometrycircumcircleperpendicular bisectorprojective geometrypower of a pointradical axisgeometry unsolved

Problem Statement

Let

K

and

L

be the points on the semicircle with diameter

AB

. Denote intersection of

AK

and

AL

as

T

and let

N

be the point such that

N

is on segment

AB

and line

TN

is perpendicular to

AB

. If

U

is the intersection of perpendicular bisector of

AB

an

KL

and

V

is a point on

KL

such that angles

UAV

and

UBV

are equal. Prove that

NV

is perpendicular to

KL

.

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