# Circles! :D

• May 5th 2007, 01:48 PM
Geometor
Circles! :D
I wonder how quick you can work this out...

http://img297.imageshack.us/img297/2415/mathwq0.th.png
• May 5th 2007, 07:49 PM
Soroban
Hello, Geometor!

Quote:

PQ and RS are parallel chords 6 cm apart.
PQ = 10 cm and RS = 14 cm.

(a) What is the shortest distance from the center to chord PQ?

(b) Find the radius of the circle.
Code:

```              * * *           *  5  T  5  *       P* - - - * - - - *Q       *        |        *                 | x       *        |        *       *        *O        *       *        |        *                 | 6-x       R*- - - - * - - - -*S         *  7  U  7  *           *          *               * * *```

Draw diameter TU through center O, perpendicular to PQ and RS.
. . Then: .TQ = 5, US = 7.
Draw radii OP = OQ = OR = OS = r.
Let x = TO, then 6 - x = OU.

In right triangle ORQ: .x² + 5² .= . .[1]

In right triangle OUS: .(6-x)² + 7² .= . .[2]

Equate [1] and [2]: .x² + 25 .= .36 - 12x + x² + 49 . . 12x .= .60

Therefore: .(a) .x = 5

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _
Substitute into [1]: .5² + 5² .= . . . . . (b) .r = 5√2

• May 6th 2007, 02:31 AM
Geometor
alright, I see. Thanks!