MathDB

Problem 8 of Finals

Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade

December 16, 2019

geometry

Problem Statement

Let

k

be a circle and

l

–line that is tangent to

k

in point

P

. On

l

from the two sides of

P

are chosen arbitrary points

A

and

B

. The tangents through

A

and

B

k

, different than

l

, intersect in point

C

. Find the geometric place of points

C

, when

A

and

B

change in such way so that

AP.BP

is a constant.