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MMO 225 Moscow MO 1952 length is mean proportional of 2 lenghts

Source:

August 8, 2019

geometryTangentsperpendicular

Problem Statement

From a point

C

, tangents

CA

and

CB

are drawn to a circle

O

. From an arbitrary point

N

on the circle, perpendiculars

ND, NE, NF

are drawn on

AB, CA

and

CB

, respectively. Prove that the length of

ND

is the mean proportional of the lengths of

NE

and

NF