Two circles with centre C1 and C2 intersect at A and B. If the radius of the circle with centre C1 is 13cm, the length of common chord of two circles is 10cm and distance between their center's is 18cm, find the radius of circle with centre C2.
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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
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