anonymous
  • anonymous
PLEASE HELP!!! Let $ABCD$ be a cyclic quadrilateral. Let $P$ be the intersection of $\overline{AD}$ and $\overline{BC}$, and let $Q$ be the intersection of $\overline{AB}$ and $\overline{CD}$. Prove that the angle bisectors of $\angle DPC$ and $\angle AQD$ are perpendicular.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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mathmath333
  • mathmath333
Let \(ABCD\) be a cyclic quadrilateral. Let \(P\) be the intersection of \(\overline{AD}\) and \(\overline{BC}\), and let \(Q\) be the intersection of \(\overline{AB}\) and \(\overline{CD}\). Prove that the angle bisectors of \(\angle DPC\) and \(\angle AQD\) are perpendicular. question
ganeshie8
  • ganeshie8
still here?

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anonymous
  • anonymous
yup
ganeshie8
  • ganeshie8
you must be knowing that opposite angles in a cyclic quadrilateral add up to 180
anonymous
  • anonymous
ohhh i see
ganeshie8
  • ganeshie8
As a start, use that to show that \(\angle DAB \cong \angle BCQ\)
anonymous
  • anonymous
oh i see where you're going! thanks so much! I'll try it out myself first and come back if i need more help!
ganeshie8
  • ganeshie8
** 1) By triangle exterior angle theorem, \(\angle DAB\cong \angle P + \angle B\). 2) Since the opposite angles in a cyclic quadrilateral add up to \(180\) : \(\angle DAB\cong \angle BCQ\) 3) From above two steps, we get \(\angle BQC \cong 180-(\angle P+\angle B) - \angle B\)
ganeshie8
  • ganeshie8
Okay, I'll let you finish it off.. good luck!
phi
  • phi
for what it is worth, here is a complicated approach

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