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 .= .r² .[1]

In right triangle OUS: .(6-x)² + 7² .= .r² .[2]

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

Therefore: .(a).x = 5

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _

Substitute into [1]: .5² + 5² .= .r² . . → . .(b).r = 5√2