P is a point outside a circle and is 26 cm away from its center. A secant PAB drawn from P intersects the circle at points A and B such that PB = 32 cm and PA = 18 cm. The radius of the circle (in cm) is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e 10
Given PO = 26 cm , PB = 32 cm , PA = 18 cm
Let OC = r cm
So, PC = (26 - r) cm
We know that PA × PB = PC × PD
⇒ 18 × 32 = (26 - r) × (26 + r)
⇒ 18 × 32 = (26)2 - r2
⇒ 576 = 676 - r2
⇒ r2 = 100
⇒ r = 10 cm