MathDB

A,B,C

and

D

are four points in that order on the circumference of a circle

K

AB

is perpendicular to

BC

and

BC

is perpendicular to

CD

X

is a point on the circumference of the circle between

A

and

D

AX

extended meets

CD

extended at

E

and

DX

extended meets

BA

extended at

F

. Prove that the circumcircle of triangle

AXF

is tangent to the circumcircle of triangle

DXE

and that the common tangent line passes through the center of the circle

K

Problem Statement