Question

The length of the common chord of two intersecting circles is 30 cm. If the radii of the two circles are 25 cm and 17 cm,find the distance between their centres.

Answer 1

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