# Math Help - Circles! :D

1. ## Circles! :D

I wonder how quick you can work this out...

2. Hello, Geometor!

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

3. alright, I see. Thanks!