Jump to content
BrainDen.com - Brain Teasers
  • 0

The infinite snowman


bonanova
 Share

Question

Consider an isosceles triangle with base 10 feet and sides 13 feet. Now imagine building a snowman inside that triangle. A snowman made of circles, not spheres. It's easy to sketch. The bottom circle is tangent to all three sides. The next circle rests on the first and is tangent to the two sides. Likewise the third, fourth, and so on. Actually, there are an infinite number of circles in our snowman. But there must be a geometric series involved, or something like one, because the snowman never gets outside the triangle. So, it's fair to ask:

What is the sum of the circumferences of all the circles?

This is actually an unadvertised "aha" puzzle, so can you give the answer without writing anything down except for the sketch?

Link to comment
Share on other sites

1 answer to this question

Recommended Posts

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
 Share

  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...