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?

2 Answers
Apr 9, 2016

Answer:

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 #CM = sqrt((CA)^2-(AM)^2)=sqrt(15^2-12^2)=sqrt81=9#
CA = radius of the circle = 15 cm and AM = (length of the chord)#/#2 = 12 cm

Apr 10, 2016

Answer:

#9cm#

Explanation:

Consider the image

enter image source here

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

enter image source here

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,

#aand b# are the right containing sides (#xand12#)

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

#rarrx^2+12^2=15^2#

#rarrx^2+144=225#

#rarrx^2=225-144#

#rarrx^2=81#

#color(green)(rArrx=sqrt81=9#