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 
vigyan-express
Free
PYST 1: SSC CGL - General Awareness (Held On : 20 April 2022 Shift 2)
25 Qs. 50 Marks 10 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 2, 2025

-> The SSC CGL Notification 2025 has been released on 9th June 2025 on the official website at ssc.gov.in.

-> The SSC CGL exam registration process is now open and will continue till 4th July 2025, so candidates must fill out the SSC CGL Application Form 2025 before the deadline.

-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.

-> TNPSC Group 4 Hall Ticket 2025 has been released on the official website @tnpscexams.in

-> HSSC Group D Result 2025 has been released on 2nd July 2025.

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

->  Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.

-> 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.

-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.

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

-> Candidates should also use the SSC CGL previous year papers for a good revision. 

->The UGC NET Exam Analysis 2025 for June 25 is out for Shift 1.

More Circle Questions

Hot Links: teen patti yas teen patti noble teen patti club apk master teen patti