Question
Download Solution PDFIn the given figure, the circle with centre O has radius 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)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The circle with center O has a radius of 10 cm
STR is a common tangent to the two circles at points R and S
RT = 16 cm
TS = 24 cm
Concept Used:
When two lines intersect each other the opposite angles are always equal
Calculations:
As we can see, Line RS and Line OP intersect each other
⇒ therefore, \(\angle\) RTO = \(\angle\) STP
Let \(\angle \) RTO be y
In \(\triangle\)ROT
⇒ tan y = \(\frac{RO}{RT}=\frac{10}{16}\)
similarly,
In \(\triangle\)STP
⇒ tan y = \(\frac{SP}{ST}=\frac{x}{24}\)
As both the angle are equal, so we get
⇒ \(\frac{10}{16}=\frac{x}{24}\)
⇒ x = \(\frac{10\times24}{16}\) = 15 cm
⇒ Hence, The radius of the circle of center P is 15 cm.
Last updated on Jun 17, 2025
-> The SSC has now postponed the SSC CPO Recruitment 2025 on 16th June 2025. As per the notice, the detailed notification will be released in due course.
-> The Application Dates will be rescheduled in the notification.
-> The selection process for SSC CPO includes a Tier 1, Physical Standard Test (PST)/ Physical Endurance Test (PET), Tier 2, and Medical Test.
-> The salary of the candidates who will get successful selection for the CPO post will be from ₹35,400 to ₹112,400.
-> Prepare well for the exam by solving SSC CPO Previous Year Papers. Also, attempt the SSC CPO Mock Tests.
-> Attempt SSC CPO Free English Mock Tests Here!