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Length of chord independent of A

Source: India Postals 2015 Set 4

November 7, 2015

geometry

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

. Prove that the length of segment

NM

doesn’t depend on point

C

.

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