Question

two circles of radius 10 centimetre and 8cm intersect and length of the common chord is 12 cm find the distance between the centre​

Answer 1

Two circles of radii 10 cm and 8 cm intersect each other at two points, and the length of the common chord is 12 cm. Find the distance between their centers.

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