Find the value of x. If necessary, round your answer to the nearest tenth. O is the center of the circle.

x = 9.8

Step-by-step explanation:

(please refer to attached)

after labeling the picture with all the known information, we can see that

OF = OR = Radius of the circle     -----(eq 1)

Consider triangle OFP,  by Pythagorean theorem,

OF² = PF²+OP²

r² = 11.5² + 11²

r² = 253.25  -----(eq 2)

Consider triangle ORQ,  by Pythagorean theorem,

OR² = RQ²+OQ²

r² = 12.5² + x²

r² = 156.25 + x²  ----(eq 3)

equating (eq 2) and (eq 3)

253.25 = 156.25 + x²    

x² = 253.25 - 156.25

x² = 97

x = √97

x = 9.8  (nearest tenth)

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