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

Home > Shapes > Geometry
Circle, Circle, Triangle, Circle! (Posted on 2004-09-08) Difficulty: 4 of 5
Consider a circle O with a diameter AB, shown here in green. Draw a second circle (red) with diameter AC, such that C is on AB. Draw an isosceles triangle with base CB and third vertex D on circle O. Draw a third circle (X), tangent to the first three figures. Prove that the line from C to the center of circle X is perpendicular to AB.

No Solution Yet Submitted by SilverKnight    
Rating: 3.5556 (9 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re: First Step | Comment 2 of 10 |
(In reply to First Step by Leming)

first, I redrew the whole idea where the red circle is half the diameter of the green circle. This expands the base of the triangle, and it does work out to be isosceles. SO, these calculations should work for any sized red circle/tringle combo.

Printed out picture and inserted new points and lines. Assuming CX to be perpindicular, the angle between CD and CX would have to be 30 degrees (60 triangles). Now, length of HX is half of CX (sin 30), which means CX is 2/3 AB. (Knowing this made it a LOT easier to draw the blue triangle on mine, and it did work out!)

more to come......


  Posted by Jim on 2004-09-09 11:44:50
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information