Circle C1 is centred at (5, 3) and its radius is equal to 7. Circle C2 is centered at (3, 5) and its radius is equal to 5. The number of common tangents of the two circles is equal to
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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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