MathDB

Problem 4 : A point

C

lies on a line segment

AB

between

A

and

B

and circles are drawn having

AC

and

CB

as diameters. A common tangent line to both circles touches the circle with

AC

as diameter at

P \neq C

and the circle with

CB

as diameter at

Q \neq C.

Prove that lines

AP, BQ

and the common tangent line to both circles at

C

all meet at a single point which lies on the circle with

AB

as diameter.

Problem Statement