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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)

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Tan | Comment 8 of 10 |

Think of it this way.

The line AC is the diameter of the Red circle, which continues on to B making it the diameter of the large green circle.

If you extend the line from C in the opposite direction it makes a tangent to the red circle. since the diameter of the green circle and the red circle are on the line AB and the the line from C is a tangent to the circle with the diameter. Thus makin the line extending from C Perpendicular to the line AB.

  Posted by Nithin on 2004-09-24 17:18:08
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