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Two circles of radii 10 cm and 17 cm intersect at two points and distance between their centers is 21 cm. Find the length of the common chord.

Asked by Topperlearning User 4th June 2014, 1:23 PM
Answered by Expert
Answer:

OP = OQ and BOQ = 90o

Let OB = x cm, OA = 21 - x cm

In rt. AOP,

OA2 + OP2 = AP2

(21 - x)2 + OP2 = 172

OP2 = 289 - (21 - x)2

In rt. BOP,

OB2 + OP2 = BP2

x2 + OP2 = 102

OP2 = 100 - x2

289 - (21 - x)2 = 100 - x2

289 - (441 + x2 - 42x) = 100 - x2

289 - 441 - x2 + 42x = 100 - x2

42x = 252

x = 6

OP2 = 100 - 62 = 64

OP = 8

PQ = 2 OP = 2 8 = 16 cm

Answered by Expert 4th June 2014, 3:23 PM
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