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

Home > Shapes > Geometry
Overlapping Triangles (Posted on 2014-02-22) Difficulty: 3 of 5
On the plane there are two triangles, each with side lengths 18, 24 and 30. If the two triangles do not completely overlap, but share the same circumcircle as well as the same inscribed circle, find the area of the region common to both triangles.

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Sketchpad Comment 1 of 1
Note that 18^2+24^2=30^2.  Actually its a 3-4-5 right triangle scaled by 6.

For two right triangles to have congruent circumcircles and congruent incircles, they must be congruent.  To have the very same circumcircle and incircle they must be reflection images over the line containing the centers of these circles.

Construct the right triangle, its circumcenter and its incenter.

Construct the line though these centers.
Reflect the triangle over these lines.
The intersection of the triangle and its reflection is a hexagon.
The area of this hexagon is 132.

  Posted by Jer on 2014-02-22 11:50:18
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 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information