MathDB

We are given three points

A,B,C

on a semicircle. The tangent lines at

A

and

B

to the semicircle meet the extension of the diameter at points

M,N

respectively. The line passing through

A

that is perpendicular to the diameter meets

NC

R

, and the line passing through

B

that is perpendicular to the diameter meets

MC

S

. If the line

RS

meets the extension of the diameter at

Z

, prove that

ZC

is tangent to the semicircle.

Problem Statement