MathDB

As shown in the figure, in the acute angle

\vartriangle ABC

AB > AC

M

is the midpoint of the minor arc

BC

of the circumcircle

\Omega

\vartriangle ABC

K

is the intersection point of the bisector of the exterior angle

\angle BAC

and the extension line of

BC

. From point

A

draw a line perpendicular on

BC

and take a point

D

(different from

A

) on that line , such that

DM = AM

. Let the circumscribed circle of

\vartriangle ADK

intersect the circle

\Omega

at point

A

and at another point

T

. Prove that

AT

bisects line segment

BC

. https://cdn.artofproblemsolving.com/attachments/1/3/6fde30405101620828d63ae31b8c0ffcec972f.png

Problem Statement