# AB is diameter whose center is O of a circle. If AC is 3 cm and BC is 4 cm, then find AB?

Feb 27, 2017

$A B = 5$

#### Explanation:

I have to assume point $C$ is on the circle too.

In geometry, if $A , B \mathmr{and} C$ are points on a circle when the line $A B$ is a diameter of the circle, then $\angle A C B$ is a right angle.

Given $A B$ is a diameter, and $A C = 3 , \mathmr{and} B C = 4$,
$\implies \angle A C B = {90}^{\circ}$
by Pythagorean theorem,
$A {B}^{2} = A {C}^{2} + B {C}^{2}$
$\implies A {B}^{2} = {3}^{2} + {4}^{2} = 25$
$\implies A B = \sqrt{25} = 5$