area of circle

Question

A 24cm long chord is 5cm away from the centre of a circle, find the length of a diameter of the circle.

Answer 1

The chord goes from one edge of the circle to

the other, but not through the center.  Draw a

line, 5 cm long, from the center of the circle to

the center of the chord, bisecting it into 2 pieces

of 12 cm each.  Then draw a radius from the

center to one of the points where the chord

touches the edge of the circle.  You now have

a right triangle with side lengths 5 cm, and

12 cm and a hypotenuse whose length is the

radius of the. circle.

 

Let's find the radius r. 

From pythagoreans theorem a²+b²=c²

5²+12²=r²

r² = 169

r = 13 cm

 

Since diameter is 2r the diameter of this

circle is d = 2(13) = 26cm

Answer 2

The answer is 13cm.  Here's how we figure that out.

 

1.  Draw a radius with the 24cm chord going through it, making a perpendicular. I usually do this from the top of the circle down to the center, so the horizontal chord will create a "cross"

2.  By rule, the chord is cut in half when it's perpendicular to a radius or diameter, so it creates 2 equal 12 cm pieces.

3.  From that intersection to the center of the circle is 5cm.

4.  Connect another radius.  This one goes from the center to where the chord intersects the circle. 

5.  This creates a perfect right triangle with legs of 5cm and 12cm.  Pythagorean Theorem (of if you know the Pythagorean triples) will give you 13cm.

 

It's way easier if I could draw a picture!  I hope this helps.  Contact me if you have any further questions!

Jeff