In the given figure, the circle with center O has a radius of 10 cm. The radius of the circle with center P is x. STR is a common tangent to the two circles at points R and S as shown in the figure. RT = 16 cm and TS = 24 cm. What is the value of x (in cm)?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 15.
Given that
The radius of a small circle (r) = OR = 10 cm
The radius of a big circle (R) = PS = x cm
⇒ RT = 16 cm, TS = 24 cm
Common Tangent RS and Center distance OP intersect each other
⇒ OTR = PTS
Let OTR = PTS = zº
In triangle OTR,
⇒ tan z = OR/RT
Similarly, in triangle PTS
⇒ tan z = SP/ST
Now, OR/RT = SP/ST
⇒ 10/16 = x/24
⇒ x = 240/16 = 15 cm