MathDB

Let

ABC

be a right triangle with

\angle B=90^{\circ}

. Point

D

lies on the line

CB

such that

B

is between

D

and

C

. Let

E

be the midpoint of

AD

and let

F

be the seconf intersection point of the circumcircle of

\triangle ACD

and the circumcircle of

\triangle BDE

. Prove that as

D

varies, the line

EF

passes through a fixed point.

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