All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
Circle perimeters (Posted on 2002-11-19) Difficulty: 2 of 5
Prove that the sum of the perimeters of the smaller circles in the Bigger circle is equal to that of the bigger circle. (The centres are on the line given which is the diameter of the bigger circle.)

See The Solution Submitted by Dulanjana    
Rating: 2.3846 (13 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Puzzle Solution Comment 9 of 9 |

Let the respective diameters of the five smaller circles be d_i, for
i=1,2,3,4,5 ; while the diameter of the bigger circle is D.

It is given that:

d_1 + d_2 + d_3 + d_4 + d_5 = D
Or, pi* (d_1 + d_2 + d_3 + d_4 + d_5) = pi*D
Or, Sum (i= 1 to 5) m_i = M_i, where m_iís is the circumference
of the ith circle for i=1,2,3,4,5 while M is the circumference of the  bigger circle.

Thus, the circumference of the bigger circle is equal to the sum of the circumferences of the five smaller circles.

  Posted by K Sengupta on 2007-05-21 10:58:24
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information