MathDB

Let

ABCD

be a trapezium of parallel sides

AD

and

BC

and non-parallel sides

AB

and

CD

Let

I

be the incenter of

ABC

. It is known that exists a point

Q \in AD

with

Q \neq A

and

Q \neq D

such that if

P

is a point of the intersection of the bisectors of

\widehat{ CQD}

and

\widehat{CAD}

then

PI \parallel AD

Prove that PI\equal{}BQ

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