There are two circles which touch each other externally. The radius of the first circle with centre O is 17 cm and radius of the second circle with centre A is 7 cm. BC is a direct common tangent to these two circles, where B and C are points on the circles with centres O and A, respectively. The length of BC is:

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 4)
View all SSC CGL Papers >
  1.  cm
  2.  cm 
  3.  cm
  4.  cm

Answer (Detailed Solution Below)

Option 2 :  cm 
super-pass-live
Free
SSC CGL Tier 1 2025 Full Test - 01
100 Qs. 200 Marks 60 Mins

Detailed Solution

Download Solution PDF

Given:

Radius of first circle = 17 cm

Radius of second circle = 7 cm

Circles touch each other externally.

BC is a direct common tangent of these two circles.

Concept used:

External tangents are lines that do not cross the segment joining the centers of the circles.

Calculation:

Join A to O and B. Join O to C. Draw AQ perpendicular to OC.

Now, AQ = BC, as they are opposite sides of rectangle AQCB.

⇒AO = AP + PQ

⇒AO = 7 + 17

⇒AO = 24 cm

⇒OQ = CO - CQ

⇒OQ = 17 - 7

⇒OQ = 10 cm

Now, applying pythagoras theorem in triangle AOQ:

 = 

⇒AQ = 

⇒AQ = 

⇒AQ = 

 ∴ The length of BC is .

Latest SSC CGL Updates

Last updated on Jul 19, 2025

-> The SSC CGL Notification 2025 has been announced for 14,582 vacancies of various Group B and C posts across central government departments.

-> CSIR NET City Intimation Slip 2025 has been released @csirnet.nta.ac.in. 

-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025 in multiple shifts.

->  Aspirants should visit the official website @ssc.gov.in 2025 regularly for CGL Exam updates and latest announcements.

-> Candidates had filled out the SSC CGL Application Form from 9 June to 5 July, 2025. Now, 20 lakh+ candidates will be writing the SSC CGL 2025 Exam on the scheduled exam date. Download SSC Calendar 2025-25!

-> In the SSC CGL 2025 Notification, vacancies for two new posts, namely, "Section Head" and "Office Superintendent" have been announced.

-> Candidates can refer to the CGL Syllabus for a better understanding of the exam structure and pattern.

-> The CGL Eligibility is a bachelor’s degree in any discipline, with the age limit varying from post to post. 

-> The SSC CGL Salary structure varies by post, with entry-level posts starting at Pay Level-4 (Rs. 25,500 to 81,100/-) and going up to Pay Level-7 (Rs. 44,900 to 1,42,400/-).

-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.

More Circle Questions

Hot Links: teen patti 51 bonus teen patti club apk teen patti apk download teen patti master gold download