Problem 7


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:


Draw the diameter AD.

Connect B and D.

ABD is a right angle.

AHC is a right angle.


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

*ABD is similar to AHC