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perpendicular wanted, tangent and secant to a circle related

Source: Champions Tournament (Ukraine) - Турнір чемпіонів - 2002 Seniors p2

September 6, 2020

geometryperpendiculartangentsecantChampions Tournament

Problem Statement

The point

P

is outside the circle

\omega

with center

O

. Lines

\ell_1

and

\ell_2

pass through a point

P

\ell_1

touches the circle

\omega

at the point

A

and

\ell_2

intersects

\omega

at the points

B

and

C

. Tangent to the circle

\omega

at points

B

and

C

intersect at point

Q

. Let

K

be the point of intersection of the lines

BC

and

AQ

. Prove that

(OK) \perp (PQ)