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O is the center of a circle of radius 8cm. The tangent at a point A on the circle cuts a line through O at B such that AB = 15 cm. Find OB

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#### Solution

Consider a circle with center O and radius OA = 8cm = r, AB = 15 cm.

(AB) tangent is drawn at A (point of contact)

At point of contact, we know that radius and tangent are perpendicular.

In ΔOAB, ∠OAB = 90°, By Pythagoras theorem

𝑂𝐵^{2} = 𝑂𝐴^{2} + 𝐴𝐵^{2}

`OB = sqrt(8^2 + 15^2)`

`=sqrt(64+225)`

`= sqrt(289)`

= 17 cm

∴ 𝑂𝐵 = 17 𝑐𝑚

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