Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

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

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.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,651

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

Offline

Pages: **1**