Question

two circle of radius 17 cm and 25 cm intersect each other at two points A and B. if the length of the common chord AB of a circle be 30 cm, find the distance between the centres of the circle.​

Answer 1

Answer:

28 cm

Step-by-step explanation:

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

⇒ 17²= PC²+ 15²

⇒ PC² = 289 - 225 = 64

⇒ PC = 8 cm

Consider ΔACO,

AO²= OC²+ AC²

⇒ 25²= OC²+ 15²

⇒ OC = 20 cm

From the figure, OP = OC + PC

= 20 + 8 = 28 cm

Hence, the distance between the centres is 28 cm

Hope it helps!