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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