MathDB

Convex angle in the plane, unique point

Source:

August 8, 2006

geometry unsolvedgeometry

Problem Statement

A convex angle

xOy

and a point

M

inside it are given in the plane. Prove that there is a unique point

P

in the plane with the following property: - For any line

l

through

M

, meeting the rays

x

and

y

(or their extensions) at

X

and

Y

, the angle

XPY

is not obtuse.