Question : In the given figure, the circle with centre O has a radius of 10 cm. The radius of the circle with centre 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)?

Option 1: 15
Option 2: 16
Option 3: 12
Option 4: 18

Question

Question : In the given figure, the circle with centre O has a radius of 10 cm. The radius of the circle with centre 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)?

Option 1: 15

Option 2: 16

Option 3: 12

Option 4: 18

Team Careers360 · Accepted Answer

Correct Answer: 15

Solution :
Given:
Radius = 10 cm
RT = 16 cm
TS = 24 cm
Since Line RS and Line OP intersect each other,
⇒ $\angle$ RTO = $\angle$ STP
Let $\angle$ RTO be $y$
In $ riangle$ ROT,
⇒ $ an y = \frac{RO}{RT} = \frac{10}{16}$
In $ riangle$ STP,
⇒ $ an y = \frac{SP}{ST} = \frac{x}{24}$
As both the angles are equal,
⇒ $\frac{10}{16} = \frac{x}{24}$
$ herefore x=\frac{240}{16}=15$
Hence, the correct answer is 15.

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