What is the radius of the circle in centimeters?

Question

A chord of a circle is 18 centimeters long, and the center of the chord is 12 centimeters from the center of the circle.

 

Please help with this one as well. Thank you!!

Answer 1

The chord of which you are speaking will be a straight line passing through the circle but not touching the center.

That means the midpoint of the chord would be 9 cm from either side of the circle.

 

Picture a circle.  Draw a straight line through it that does not touch the center

Now draw a straight line from the middle of the chord to the center of the circle

 

Then draw a straight line from the center of the circle to one of the points where your chord touches the outer edge of the circle.  We have just drawn a right triangle with leg lengths of 9 cm and 12 cm ... the other line (center to outer edge) is the hypotenuse of the triangle which will also constitute a radius of the circle. 

 

Use the Pythagorean theorem  a²+ b² = c² where c is the hypotenuse

 

9²+ 12² = r²   

 

r² = 81 + 144

 

r² = 225

 

r = √225

 

r = 15 cm

 

The circle has a radius of 15 cm