In the figure, AB//CD and they are 4 cm apart. P and Q are the mid-points of AB and CD respectively. If AB=16 cm and CD=12 cm, find: (a) the length of OP (b) the radius of the circle.

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In the figure, AB//CD and they are 4 cm apart. P and Q are the mid-points of AB and CD respectively. If AB=16 cm and CD=12 cm, find: (a) the length of OP (b) the radius of the circle.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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I have think about it but I cannot do furthermore...
Right triangle AOP has legs AP and OP and hypotenuse OA Right triangle COQ has legs CQ and OQ and hypotenuse OC Because they're both radii, OA = OC = r For right triangle AOP, (OP)^2 + (AP)^2 = r^2 For right triangle COQ, (CQ)^2 + (OQ)^2 = r^2 By substitution, (OP)^2 + (AP)^2 = (CQ)^2 + (OQ)^2 Substitue values we know: (OP)^2 + 64 = 36 + (OP + 4)^2 (OP)^2 + 64 = 36 + (OP)^2 + 8(OP) + 16 Subtract (OP)^2 from both sides 64 = 36 + 8(OP) + 16 8(OP) = 12 OP = 1.5
wait a moment....
got it. then I know part b :) thank you
(AP)^2 + (OP)^2 = r^2 64 + (1.5)^2 = r^2 r^2 = 66.25 r^2 = 265/4 r = sqrt(265)/2
thank you very much
You're very welcome.

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