Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
4.4k views
in Circles by (23.7k points)
closed by

Three circles touch each other externally and all the three touch a line. If two of them are equal and the third has radius 4 cm. Find the radius of the equal circles.

1 Answer

+1 vote
by (22.8k points)
selected by
 
Best answer

     

Consider the condition: what is the length of the common tangent when two circles of radii r1 and r2 touch externally? 

Here AB (the common tangent) 

= O′C = \(\sqrt{OO'^2 -OC^2}\) 

\(\sqrt{(r_1+r_2)^2 - (r_1 -r_2)^2}\) 

\(\sqrt {4r_1\,r_2}\) = \(2\sqrt{r_1\,r_2}\) 

Therefore, according to the given figure, PR is the length of the common tangent to circle of radii r and 4.

∴ PQ = \(2\sqrt{4r}\) = \(4\sqrt{r}\) 

QR = \(2\sqrt{4r}\) = \(4\sqrt{r}\) 

∵ PR = PQ + QR 

∴ 2r = \(4\sqrt{r}\) + \(4\sqrt{r}\)  

⇒ r = \(4\sqrt{r}\) 

⇒ r2 = 16r 

r = 16 cm.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...