Question : P is a point outside a circle with centre O, and it is 14 cm away from the centre. A secant PAB drawn from P intersects the circle at points A and B such that PA = 10 cm and PB = 16 cm. The diameter of the circle is:
Option 1: 10 cm
Option 2: 13 cm
Option 3: 11 cm
Option 4: 12 cm
Correct Answer: 12 cm
Solution :
Given, OP = 14 cm, PA = 10 cm, PB = 16 cm
Let the radius of the circle be r cm.
⇒ OQ = OE = r cm
⇒ PE = (14 – r) and PQ = (14 + r)
As we know,
PE × PQ = PA × PB
⇒ (14 – r) (14 + r) = 10 × 16
⇒ 14
2
– r
2
= 160
⇒ 196 – r
2
= 160
⇒ r
2
= 196 – 160 = 36
⇒ r = 6 cm
So, the diameter of the circle = 2 × 6 = 12 cm
Hence, the correct answer is 12 cm.
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