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## #1 2014-07-02 02:33:44

rptamin
Member
Registered: 2014-07-02
Posts: 3

### geometry problem

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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## #2 2014-07-02 06:16:12

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,566

### Re: geometry problem

hi rptamin

Welcome to the forum.

Try this:  let x be the angle at A and y be the angle at D.

Using the angle sum of a triangle, the cyclic property that opposite angles add to 180, and the bisector property you can work out all the angles in the diagram in terms of x and y.  Keep working them out until you get the angle you want = 90.

You'll need a large diagram because it gets complicated writing in expressions like  (x+y)/2 - 90 for one of a bisected pair.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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