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Locus of a tangent point

Source: 1962 All-Soviet Union Olympiad

January 15, 2018

geometryLocusRussia

Problem Statement

Given a fixed circle

C

and a line L through the center

O

of

C

. Take a variable point

P

on

L

and let

K

be the circle with center

P

through

O

. Let

T

be the point where a common tangent to

C

and

K

meets

K

. What is the locus of

T

?

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