R is a point outside a circle and is 18 cm away from its centre. A secant drawn from the point R intersects the circle at points A and B in such a way that RA = 7 cm and AB = 5 cm. The radius of the circle (in cm) is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. .
OR = 18 cm, RA = 7 cm and AB = 5 cm
RB = 7 + 5 = 12 cm
Extend OR to the point P.
Let the radius of the circle = r cm
OP = OQ = r cm
So, PR = 18 + r
Also, QR = 18 - r
The intersecting secants theorem states that when two secants intersect at an exterior point, the product of the one whole secant segment and its external segment is equal to the product of the other whole secant segment and its external segment.
RA × RB = PR × QR
⇒ 7 × 12 = (18 + r)(18 - r)
⇒ 324 - r2 = 84
⇒ r2 = 324 - 84 = 240
⇒ r = √240 = 4√15
Therefore, the radius of the circle is 4√15 cm.