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 Circle, Circle, Triangle, Circle! (Posted on 2004-09-08)
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)

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 First Step | Comment 1 of 10

First, draw the diagram on a sheet of paper.  Add a new point E as the center of AB.  This is the center of the big circle.  Then add point F as the center of AC. This is the center of the medium circle.  Connect F to X and label the tangent of the two circles as G. Next add H as the tangent between the circle X and the triangle.

Now connect X to H and realize the obvious that CHX is a right triangle.  Look at the diagram for 60 minutes, and then type in the results.  Next step:  Sit back and wait for someone who remembers all of their geometry to post a comment.

Thats what I did.

 Posted by Dan Blume on 2004-09-09 02:39:30

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