P is a point outside a circle and is 26 m away from its center. A secant PAB has drawn from 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
OA is the radius of a circle PA = 18 cm and PB = 32 cm
Then AB = 32 - 18 = 14
then BD = AD = 7 cm
In the triangle ODP ,
(OD)2 = (OP)2 - (DP)2
(OD)2 = (26)2 - (25)2
OD = √51
Then in triangle OAD,
r2 = (OD)2 + (AD)2
r2 = (√51)2 + (7)2
r2 = 51 + 49 = 100
r = 10 cm