Question

Two circles of radius 17cm and 25 cm intersect each other at two points A and B. If the length of common chord AB of the circles be 30cm find the distance between the centres of the circles.

Answer 1

hola there,

Given length of common chord AB = 30 cm
Let the radius of the circle with centre O is OA = 25 cm
Radius of circle with centre P is AP = 17 cm
From the figure,, OP⊥ AB
⇒ AC = CB
∴ AC = 15 cm (Since AB = 30 cm)
In ΔACP, AP2�= PC2�+ AC2��� [By Pythagoras theorem]
⇒ 172�= PC2�+ 152��
⇒ PC2�= 289 – 225 = 64
⇒ PC = 8 cm
Consider ΔACO
AO2�= OC2�+ AC2������ ������������� [By Pythagoras theorem]
⇒ 252�= OC2�+ 152��
⇒ OC2�= 625 – 225 = 400
⇒ OC = 20 cm
From the figure, OP = OC + PC
�������������������������������������� = 20 + 8 = 28 cm�
Hence, the distance between the centres is 28 cm

Answer 2

distance between the centre is 28 cm