MathDB

APT and KPC are tangent [Iran TST 2010]

Source:

June 9, 2010

geometrycircumcircleincentergeometric transformationparallelogramangle bisectorgeometry proposed

Problem Statement

Let

M

be an arbitrary point on side

BC

of triangle

ABC

W

is a circle which is tangent to

AB

and

BM

T

and

K

and is tangent to circumcircle of

AMC

P

. Prove that if

TK||AM

, circumcircles of

APT

and

KPC

are tangent together.