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Two tangents and bisection

Source: 2022 Nigeria MO Round 3/Problem 4

April 17, 2022

geometryNigeria MO

Problem Statement

Let

PT

and

PB

be two tangents to a circle,

T

and

B

on the circle.

AB

is the diameter of the circle through

B

and

TH

is the perpendicular from

T

to

AB

,

H

on

AB

. Prove that

AP

bisects

TH

.

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