MathDB

locus of M

Source: turkey TST 2007

April 10, 2007

ratiogeometrysimilar trianglesangle bisectorgeometry proposed

Problem Statement

Two different points

A

and

B

and a circle

\omega

that passes through

A

and

B

are given.

P

is a variable point on

\omega

(different from

A

and

B

).

M

is a point such that

MP

is the bisector of the angle

\angle{APB}

(

M

lies outside of

\omega

) and

MP=AP+BP

. Find the geometrical locus of

M

.

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