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Let $ABCD$ be a cyclic quadrilateral. Let $P$ be the intersection of $\overleftrightarrow{AD}$ and $\overleftrightarrow{BC}$, and let $Q$ be the intersection of $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$. Prove that the angle bisectors of $\angle DPC$ and $\angle AQD$ are perpendicular.
 Apr 7, 2019
 #1
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How do I prove that angle DCP equals 180 - angle DAB?

 Apr 7, 2019
 #2
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Inscribed angles in a circle encompass an arc 2x their measure....opposite angles encompass the entire circle perimeter.

 

Say angle A is opposite angle B.....

    then     2A + 2B = 360

                 2A = 360 - 2B

Divide throught by 2

                    A = 180-B                       Does that clear things up?

 Apr 7, 2019

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