MathDB

Easy Geometry

Source: 2015 JBMO TST - Macedonia, Problem 2

December 31, 2015

circlestangentcyclic quadrilateralgeometry

Problem Statement

A circle

k

with center

O

and radius

r

and a line

p

which has no common points with

k

, are given. Let

E

be the foot of the perpendicular from

O

to

p

. Let

M

be an arbitrary point on

p

, distinct from

E

. The tangents from the point

M

to the circle

k

are

MA

and

MB

. If

H

is the intersection of

AB

and

OE

, then prove that

OH=\frac{r^2}{OE}

.

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