Circle problem

Jaspworld said:
Look at http://www.doitpoms.ac.uk/tlplib/slip/i ... _ratio.php

How does the top side of the triangle equal (1/2 a)/ cos 30. Remember 2a=r.
Click to expand...

If you join the centers of three equal circles(spheres) - they form an equilateral triangle - with 60° angles between those. The bisector of that triangle will make 30° angles with adjacent sides.

Get hold of few billiard balls and try to stacke those as you visualize - you should see it.
 
Oh man..

I don't see it. How can you connect the three circles and get a equilateral triangle. The bottom side is clearly more than 2r.

Help me visualize!
 
Jaspworld said:
How can you connect the three circles and get a equilateral triangle.
Click to expand...
Through any three points, you can place a plane. So think of the three circle-centers as lying in that plane. Draw the lines connecting the centers. This is a triangle. Etc.

Eliz.
 
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