# Arcs

• Jun 30th 2010, 10:45 PM
soni
Arcs
Please give me full solution of this question with image also:
If X and Y are the middle points of arcs AB and CD of circle and sigment joining by X and Y cuts the AB and CD at point P and Q then prove that AP=AQ
• Jul 1st 2010, 05:24 AM
Soroban
Hello, soni!

There must be a typo . . . The problem makes no sense.

Quote:

$\displaystyle X\text{ and }Y$ are midpoints of arcs $\displaystyle AB\text{ and }CD$ of a circle
and segment $\displaystyle XY$ cuts chords $\displaystyle AB\text{ and }CD$ at $\displaystyle P\text{ and }Q$, resp.

Prove: .$\displaystyle AP=AQ$ . ??

Code:

                  C           A  * * o           o      |  *         * |      |    *       *  |      |      *           |      |       *  |P      |Q      *     X o - + - - - + - - - o Y       *  |      |      *           |      |       *  |      |      *         * |      |    *           o      |  *           B  * * o                   D

Draw segment $\displaystyle AQ.$

We can see that $\displaystyle AP$ is never equal to $\displaystyle AQ.$