Question

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

It is given that

OA = 10cm and AB = 12 cm

So we get

AD = ½ × AB

By substituting the values

AD = ½ × 12

By division

AD = 6cm

Consider △ ADO

Using the Pythagoras theorem

OA² = AD² + OD²

By substituting the values we get

10² = 6² + OD²

On further calculation

OD² = 10² – 6²

So we get

OD² = 100 – 36

By subtraction

OD² = 64

By taking the square root

OD = √64

So we get

OD = 8cm

We know that O’A = 8cm

Consider △ ADO’

Using the Pythagoras theorem

O’A² = AD² + O’D²

By substituting the values we get

8² = 6² + O’D²

On further calculation

O’D² = 8² – 6²

So we get

O’D² = 64 – 36

By subtraction

O’D² = 28

By taking the square root

O’D = √28

We get

O’D = 2 √7

We know that

OO’ = OD + O’D

By substituting the values

OO’ = (8 + 2 √7) cm

Therefore, the distance between their centres is (8 + 2 √7) cm.