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Question
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
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
๐๐ต2 = ๐๐ด2 + ๐ด๐ต2
`OB = sqrt(8^2 + 15^2)`
`=sqrt(64+225)`
`= sqrt(289)`
= 17 cm
∴ ๐๐ต = 17 ๐๐
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