Question

9. Two circles of radii 10 cm and 8 cm
intersect each other and the length of the
common chord is 12 cm. Find the distance
between their centres.​

Answer 1

Step-by-step explanation:

Given length of common chord AB=12 cm

Let the radius of the circle with centre O is OA=10 cm

Radius of circle with centre P is AP=8 cm

From the figure, OP⊥AB

⇒AC=CB

∴AC=6 cm (Since AB=12 cm)

In ΔACP,

AP

2

=PC

2

+AC

2

[By Pythagoras theorem]

⇒8

2

=PC

2

+6

2

⇒PC

2

=64–36=28

PC=2

7

cm

Consider ΔACO,

AO

2

=OC

2

+AC

2

[By Pythagoras theorem]

⇒10

2

=OC

2

+6

2

⇒OC

2

=100−36=64

⇒OC=8 cm

From the figure, OP=OC+PC=8+2

7

cm

the distance between the centres is (8+2

7

) cm.