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.
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
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