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Construction of similar triangle

Source: 54 Polish MO 2003 Second Round - Second Day Problem 5

April 21, 2018

geometryPolandTriangleconstructionsimilar triangles

Problem Statement

Point

A

lies outside circle

o

of center

O

. From point

A

draw two lines tangent to a circle

o

in points

OF

and

C

. A tangent to a circle

o

cuts segments

AB

and

BP

in points

E

and

QC

, respectively. Lines

OE

and

OF

cut segment

BC

in points

P

and

Q

, respectively. Prove that from line segments

BP

,

PQ

,

QC

can construct triangle similar to triangle

AEF

.

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