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Two circle of a radii 10cm and 8cm intersect and the length of the common chord is 12cm find the distance between their centers?
Verified Answer
Two circle of a radii 10cm and 8cm intersect and the length of the com...
Center of circles= O and O'
Radii = 10 and 8cm
common chord= PQ
OP= 10cm
O'P = 8cm
PQ= 12cm
PL= 1/2PQ
= 1/2 x 12
= 6cm

In right angle triangle OLP 

OP^2 = OL^2 + LP^2
OL= √OP^2 - LP^2
= √10^2- 6^2
= √64
= 8cm

In right angle triangle O'LP

O'P^2= O'L^2 - LP^2
O'L= √O'P^2 - LP^2
= √8^2 - 6^2
= √28
= 5.29 cm

OO'= 8 + 5.29 
= 13.29 cm
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Two circle of a radii 10cm and 8cm intersect and the length of the common chord is 12cm find the distance between their centers?
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