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.

mABD=mAHC

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

*ABD is similar to AHC

*