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Prove the following theorem: The product of two sides of a triangle is equal to the product of the altitude of the third side and the diameter of the circumscribed circle of the triangle.

[Problem submitted by Steve Lee, LACC Professor of Mathematics. Source: Many geometry books.]

**Solution for Problem 7: **

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Draw the diameter AD.

Connect B and D.

ABD is a right angle.

AHC is a right angle.

_{}mABD=mAHC

mACH=mADB, since they face the same arc AB.

_{}_{}ABD is similar to _{}AHC

_{}_{}