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locus of vertice of isosceles triangle (V Soros Olympiad 1998-99 Round 2 9.5)

Source:

May 25, 2024

geometryLocusisosceles

Problem Statement

An angle with vertex

A

is given on the plane. Points

K

and

P

are selected on its sides so that

AK + AP = a

, where

a

is a given segment. Let

M

be a point on the plane such that the triangle

KPM

is isosceles with the base

KP

and the angle at the vertex

M

equal to the given angle. Find the locus of points

M

(as

K

and

P

move).