1 View

Question : The distance between the centres of two circles of radii 3 cm and 8 cm is 13 cm. If the points of contact of a direct common tangent to the circles are P and Q, then the length of the line segment PQ is:

Option 1: 11.9 cm

Option 2: 12 cm

Option 3: 11.58 cm

Option 4: 11.5 cm


Team Careers360 15th Jan, 2024
Answer (1)
Team Careers360 23rd Jan, 2024

Correct Answer: 12 cm


Solution : Given: Two circles of radii 3 cm and 8 cm, the distance between the centres = 13 cm and PQ is the direct common tangent.
We know,
The length of the direct common tangent of two circles = $\sqrt{d^2-(r_1-r_2)^2}$
Here, the distance between the centres($d$) = 13 cm, radius($r_1$) = 8 cm and radius($r_2$) = 3 cm
So, the length of the direct common tangent(PQ)
= $\sqrt{13^2-(8-3)^2}$
= $\sqrt{13^2-5^2}$
= $\sqrt{144}$
= $12\ \text{cm}$
Hence, the correct answer is 12 cm.

How to crack SSC CHSL

Candidates can download this e-book to give a boost to thier preparation.

Download Now

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books