AB is a chord of a circle with 0 as centre. C is a point

Home » Aptitude » Plane Geometry » Question

AB is a chord of a circle with 0 as centre. C is a point on the circle such that OC ⊥ AB and OC intersects AB at P. If PC = 2 cm and AB = 6 cm then the diameter of the circle is

1. 6 cm
2. 6.5 cm
3. 13 cm
4. 12 cm

Correct Option: B

On the basis of question we draw a figure of a circle with centre O ,

OC ⊥ AB
∴ AP = PB = 3 cm
PC = 2 cm
If OA = OC = r cm
then, OP = (r – 2) cm.
From ∠ OAP,
OA² = AP² + OP²
⇒ r² = 3² + (r – 2)²
⇒ r² – (r – 2)² = 9
⇒ r² – r² + 4r – 4 = 9

⇒ 4r = 13 ⇒ r =	13	= cm.
	4

∴ Diameter of circle = 2 ×	13	=	13	cm. = 6.5 cm.
	4		2