MathDB

Internally tangent circles

Source: Turkey TST 2002 - P5

April 6, 2013

geometrygeometric transformationhomothetyreflectionrotationgeometry proposedInversion

Problem Statement

Two circles are internally tangent at a point

A

. Let

C

be a point on the smaller circle other than

A

. The tangent line to the smaller circle at

C

meets the bigger circle at

D

and

E

; and the line

AC

meets the bigger circle at

A

and

P

. Show that the line

PE

is tangent to the circle through

A

C

, and

E