MathDB

In the plane, the point

M

is the midpoint of a line segment

[AB]

and

\ell

is an arbitrary line that has no has a common point with the line segment

[AB]

(and is also not perpendicular to

[AB]

). The points

X

and

Y

are the perpendicular projections of

A

and

B

onto

\ell

, respectively. Show that the circumscribed circles of triangle

\vartriangle AMX

and triangle

\vartriangle BMY

have the same radius.

Problem Statement