Tangents

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Circle O is tangent to AB at A, and angle ABD = 90 degrees. If AB = 12 and CD = \(30\), find the radius of the circle.

Guest Feb 16, 2022

CPhill · Answer 1 · 2022-02-16T06:08:37

Let E be the midpoint of chord CD

Then OE is perpendicular to DC

And OED forms a right triangle with DE = 15 , OE = 12

And by the Pythagorean Theorem, OD is a radius = sqrt ( DE^2 + OE^2 ) = sqrt ( 15^2 + 12^2 ) =

sqrt [ 225 + 144] = sqrt (369) ≈ 19.21