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.
m
ABD=m
AHC
m
ACH=m
ADB, since they face the same arc AB.
ABD is similar to 
AHC
