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Circle in hypotenuse (Posted on 2003-11-14) Difficulty: 3 of 5
Prove that if you draw a right triangle and then draw a circle with its center on the hypotenuse's midpoint such that it intersects at least 1 vertex, it will in fact intersect all three.

See The Solution Submitted by Antonio    
Rating: 2.5000 (4 votes)

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Solution another way | Comment 3 of 13 |
Place the center of the hypotenuse at the origin of cartesion coordinates, and make the legs parallel to the coordinate axes. The equation of a circle with origin at the center will be x²+y²=r² where r is half the length of the hypotenuse. By symmetry the coordinates of the vertices that do not match, will be the negative of each other and also on this circle, where the squaring removes the effect of the sign.
  Posted by Charlie on 2003-11-14 15:55:04
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