two equal circles of radius 10cm intersect each other at the length of their common chord is 12cm determine the distance between the centres of two circle
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Answer:
Let O and O' be the centers of the circle of radii 10 cm and 8 cm respectively.
Let PQ be their common chord.
We have,
OP = 10 cm
O'P = 8 cm
PQ = 12 cm
(Perpendicular from the center of the circle to a chord bisects the chord).
In right OLP, we have
OP2 = OL2 + PL2
In right O'LP we have
(O'P)2 = (PL)2 + (O'L)2
OO' = 8 + 5.29
= 13.29 cm
Explanation:
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