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Question

-1

586

2

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

Guest · Answer 1 · 2019-04-07T01:30:04

How do I prove that angle DCP equals 180 - angle DAB?

ElectricPavlov · Answer 2 · 2019-04-07T04:20:40

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?