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anonymous

  • one year ago

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.

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  1. anonymous
    • one year ago
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  2. mathmath333
    • one year ago
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    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

  3. ganeshie8
    • one year ago
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    still here?

  4. anonymous
    • one year ago
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    yup

  5. ganeshie8
    • one year ago
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    you must be knowing that opposite angles in a cyclic quadrilateral add up to 180

  6. anonymous
    • one year ago
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    ohhh i see

  7. ganeshie8
    • one year ago
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    As a start, use that to show that \(\angle DAB \cong \angle BCQ\)

  8. anonymous
    • one year ago
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    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!

  9. ganeshie8
    • one year ago
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    ** 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 \(\angle BQC \cong 180-(\angle P+\angle B) - \angle B\)

  10. ganeshie8
    • one year ago
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    Okay, I'll let you finish it off.. good luck!

  11. phi
    • one year ago
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    for what it is worth, here is a complicated approach

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