Question

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

Answer 1

Let O and O' be the centres of two circles with radii 10 cm and 8 cm respectively.
So, OP = 10 cm, O'P = 8 cm
and PQ = 12 cm
then PL = `1/2"PQ"` = 6 cm

In Δ OLP,
OP2 = OL2 + LP2
⇒ OL2 = OP2 - LP2
⇒ OL = `sqrt((10)^2 - (6)2) = sqrt64`= 8 cm

In O'LP,
O'L = `sqrt("O'P"^2 - "LP"^2)`
O'L = `sqrt(8^2 - 6^2)`
O'L = `sqrt(64 - 36)`
O'L = `sqrt(28)` cm
O'L = 5.29 cm

Distance between centres
OO' = OL + LO'
OO' = (8 + 5.29) cm
OO' = 13.29 cm