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CTK Exchange
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Member since Nov-5-08
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Nov-05-08, 11:19 PM (EST) |
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"Pythoagore & intersecting chord theorem"
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Hello there, I find the seventy and so proofs of Pythagore's theorem really worth of interest. A great thank to those who contributed to it ! I'd like to make a suggestion : the last proof show an elegant appication of the intersection chord theorem, I think I have an even shorter, similar to proof #61. A picture would definitely help shortening what's coming :-) Let A a point outside of a circle of radius r and center O and T on the circle such as (AT) is tangent to the circle. If I and J are on the circle such as the straight lines (AO) and (IJ) are the same, then by the tranversal chord theorem one has AT*AT = AI*AJ, ie AT˛=AO˛-r˛, QED. |
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