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O is the centre of a circle of radius 6 cm. P is a point such that OP = 10 cm and OP intersects the circle at T and PC, PD are two tangents drawn to the circle. If AB is the tangent to the circle at T, find the length AB. |
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Answer» O is the centre of a circle of radius 6 cm. P is a point such that OP = 10 cm and OP intersects the circle at T and PC, PD are two tangents drawn to the circle. If AB is the tangent to the circle at T To Find : the length ABSolution:OC = OD = OT = 6 cm = RadiusOP = 10 cm PT = OP - OT = 10 - 6 = 4 cm PC is TangentHence OP² = OC² + PC²=> 10² = 6² + PC²=> 100 = 36 + PC²=> 64 = PC²=> PC = 8similarly PD = 8 ( PC = PD Equal tangents )Let say AT = x CMTHEN AC = AT = x ( Equal Tangent )AP = PC - AC=> AP = 8 - x AT = c∠ATP = 90° as ∠OTA = 90° AP² = AT² + PT²=> (8 - x)² = x² + 4²=> 8² + x² - 16x = x² + 16=> 64 - 16x = 16=> 4 - x = 1=> x = 3AT = 3 cmSimilarly BT = 3 cmAB = AT + BT = 3 + 3 = 6 cmAB = 6 cmlength AB = 6 cmLearn More:the length of tangent to a circle which is 13cm distance from the ...brainly.in/question/14791961If ab is a tangent drawn from an point b to a circle with centre c qnd ...brainly.in/question/13581846 |
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