MathDB

intesecting tangents to create a segment of constant length

Source: 2014 Sharygin Geometry Olympiad Final Round 10.2

August 3, 2018

geometrytangentconstantSegment

Problem Statement

A circle, its chord

AB

and the midpoint

W

of the minor arc

AB

are given. Take an arbitrary point

C

on the major arc

AB

. The tangent to the circle at

C

meets the tangents at

A

and

B

at points

X

and

Y

respectively. Lines

WX

and WY meet AB at points

N

and

M

respectively. Prove that the length of segment

NM

does not depend on point

C

.
(A. Zertsalov, D. Skrobot)