MathDB

Italian mathematical olympiad 2002, problem 3

Source:

February 13, 2012

geometrycircumcircletrigonometryperpendicular bisectorgeometry proposed

Problem Statement

Let

A

and

B

are two points on a plane, and let

M

be the midpoint of

AB

. Let

r

be a line and let

R

and

S

be the projections of

A

and

B

onto

r

. Assuming that

A

M

, and

R

are not collinear, prove that the circumcircle of triangle

AMR

has the same radius as the circumcircle of

BSM