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


Team Careers360 11th Jan, 2024
Answer (1)
Team Careers360 14th Jan, 2024

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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