Question

13. Two circles of radii 10 сmand 6 cm intersect at two points and the distance between their
centers is 8 cm. Find the length of the common chord.​

Answer 1

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