Question

in order to create a pattern for a blanket, ming needs to use two congruent circles as shown. if ( op = 31 ) inches and ( ab = 5 ) inches, what is the radius of one of the circles?

• ( 15.5 ) in.
• ( 18 ) in.
• ( 16.5 ) in.
• ( 13 ) in.

Explanation:

Step1: Define radius as $r$

Let $OA = PB = r$ (radii of congruent circles)

Step2: Express $OP$ in terms of $r$

$OP = OA + PB - AB$
Substitute values: $31 = r + r - 5$

Step3: Solve for $r$

Simplify: $31 = 2r - 5$
Rearrange: $2r = 31 + 5 = 36$
Calculate: $r = \frac{36}{2} = 18$

Answer:

B. 18 in.