Two circles of radii 7 cm and 9 cm intersect at the point A and B. If AB = 10 cm and the distance between the centers of the circles is x cm, then the value of x is?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 2(√6 + √14) cm
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Understanding |
Application |
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Perpendicular drawn from the centre to the chord of a circle bisects the chord. Given: Radius AX = 7 cm and AY = 9 cm AB = 10 cm Then, AO = 10/2 = 5 cm
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In right angle triangle AXO: XO2 = AX2 – AO2 XO2 = 72 – 52 XO = √(49-25) XO = √24 XO = 2√6 cm In right angle triangle AYO: YO2 = AY2 – AO2 YO2 = 92 – 52 YO = √(81 - 25) YO = √56 YO = 2√14 cm Hence, XY = XO + OY = 2√6 + 2√14 = 2(√6 + √14) cm |
