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.

Guest Apr 7, 2019

#2**+1 **

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?

ElectricPavlov Apr 7, 2019