MathDB

perpendicularity wanted related to tangents in a circle

Source: 2007 Balkan Shortlist BMO G1 - Romania

April 5, 2020

geometryperpendicularTangentscircle

Problem Statement

Let

\omega

be a circle with center

O

and let

A

be a point outside

\omega

. The tangents from

A

touch

\omega

at points

B

, and

C

. Let

D

be the point at which the line

AO

intersects the circle such that

O

is between

A

and

D

. Denote by

X

the orthogonal projection of

B

onto

CD

, by

Y

the midpoint of the segment

BX

and by

Z

the second point of intersection of the line

DY

with

\omega

. Prove that

ZA

and

ZC

are perpendicular to each other.

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