CBSE Class 9 Answered
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 | 04 Jun, 2014, 01:23: PM
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 | 04 Jun, 2014, 03:23: PM
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