In the given figure a point P outside the circle a secant is drawn that cuts the circle at B and A and another secant is drawn that pass through the centre of circle and cuts it at D and C if PB = 8, AB = 12 and OP = 18 then find the radius of circle.

Question

Question

Answer 1

F1 Vaibhav Soni 12.4.21 Pallavi D2

Given:

AB = 12, PB = 8, and OP = 18

⇒ PA = AB + PB

⇒ PA = 8 + 12

⇒ PA = 20

⇒ PD = 18 - r

⇒ PC = 18 + r

Where, r = radius of circle

Formula Used:

In two chords AB and CD intersect at outer point of P then,

PB × PA = PD × PC

Calculation:

PB × PA = PD × PC

⇒ 8 × 20 = (18 - r)(18 + r)

⇒ 160 = 18² - r²

^⇒r² = 324 - 160

⇒ r² = 164

⇒ r = \(\sqrt {164} \)

⇒ r = \(2\sqrt {41} \)

∴ The radius of circle is \(2\sqrt {41} \)

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