Find the distance between the chord and the center of a circle if the radius is 26m and the chord is 48m long.

Question

I'm using acellus and every answer I put in is wrong

Answer 1

Draw a circle, and label the center.

Draw the radius of 26m, diameter of 52m.

Now draw a chord of 48m.  Half the chord is 24m.  These lines should be parallel.

 

Draw a line from the center to the point where the chord touches the circle.

 

Now draw a line perpendicular to the diameter and the chord at the point where the chord and circle intersect.

 

You've now created a right triangle where the hypothenuse is the diagonal line from the circle center to the point where the chord meets the circle.  It's measure is 26m.  The base of the triangle is half the chord, 24m.  And, the height of the triangle is the distance between the diameter/radius and the chord.  This is what we need to find, x.

 

Use the pythagorean theorem to solve

x² + 24² = 26²

x² + 576 = 676

x² = 100

x = 10

 

The chord is 10 m from the center of the circle.