# Suppose the diameter of a circle is 30 centimeters long and a chord is 24 centimeters long. How do you find the distance between the chord and the center of the circle?

Apr 9, 2016

9 cm.

#### Explanation:

If AB is the chord, M is its midpoint and C is the center of the circle,
the distance between the chord and the center is $C M = \sqrt{{\left(C A\right)}^{2} - {\left(A M\right)}^{2}} = \sqrt{{15}^{2} - {12}^{2}} = \sqrt{81} = 9$
CA = radius of the circle = 15 cm and AM = (length of the chord)$/$2 = 12 cm

Apr 10, 2016

$9 c m$

#### Explanation:

Consider the image

Let the distance between the chord and centre of the circle be $x$

We need to find $x$

For that we need to recreate this image

Now we have formed a right angle triangle

Now the problem has become easy!

Use Pythagoras theorem

color(blue)(a^2+b^2=c^2

Where,

$a \mathmr{and} b$ are the right containing sides ($x \mathmr{and} 12$)

$c$ is the Hypotenuse (longest side-$15$)

$\rightarrow {x}^{2} + {12}^{2} = {15}^{2}$

$\rightarrow {x}^{2} + 144 = 225$

$\rightarrow {x}^{2} = 225 - 144$

$\rightarrow {x}^{2} = 81$

color(green)(rArrx=sqrt81=9