Chapter 8.4, Problem 22PSC

Solution

To Prove: Square of CD is equal to the product of AD and DB.

Given information: $\angle ACB$ is a right angle and $\overline{CD}$ is an altitude are provided in the question which will help to find the solution.

Proof: According to property associated with altitudes in right angled triangle.

So, by using hypotenuse leg property,

➔ $\Delta ADC\sim \Delta CDB$

So, $\frac{CD}{AD}=\frac{BD}{CD}$

➔ $C{D}^2=BD\times AD$