MathDB

Let

ABC

be a triangle and

AB\ne AC

D

is a point on

BC

such that BA \equal{} BD and

B

is between

C

and

D

. Let

I_{c}

be center of the circle which touches

AB

and the extensions of

AC

and

BC

CI_{c}

intersect the circumcircle of

ABC

again at

T

. If \angle TDI_{c} \equal{} \frac {\angle B \plus{} \angle C}{4} then find

\angle A

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