MathDB

Let

ABC

be a triangle and let

M

be the midpoint of the side

BC

. The circle with radius

MA

centered in

M

meets the lines

AB

and

AC

again at

B^{'}

and

C^{'}

, respectively , and the tangents to this circle at

B^{'}

and

C^{'}

meet at

D

. Show that the perpendicular bisector of the segment

BC

bisects the segment

AD

Problem Statement