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Locus of point in the line connecting foot of tangents

Source: 2012 Indonesia Round 2 TST 4 Problem 2

March 18, 2012

geometry proposedgeometry

Problem Statement

Let

\omega

be a circle with center

O

, and let

l

be a line not intersecting

\omega

.

E

is a point on

l

such that

OE

is perpendicular with

MB

. Let

M

be an arbitrary point on

M

different from

E

. Let

A

and

B

be distinct points on the circle

\omega

such that

MA

and

MB

are tangents to

\omega

. Let

C

and

D

be the foot of perpendiculars from

E

to

MA

and

MB

respectively. Let

F

be the intersection of

CD

and

OE

. As

M

moves, determine the locus of

F

.

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