Question

In a circle of radius 6cm, Calculate to

one significant figure the length of a
chord which is 4cm from the centre of the
Circle?

Answer 1

9 cm to 1 s. f.

Explanation:

If we draw 2 radii from a point on the circle to both ends of the chord, we get an isosceles triangle with height 4 cm and equal sides of 6 cm. This consists of 2 right triangles of height 4 , hypotenuse 6 cm and base equal to half the length of the chord.

By Pythagoras:

6^2 = 4^2 + b^2 where b = base.

b = √(6^2 - 4^2)

= √20

= 4.472 cm

So, the length of the chord = 2 * 4.472

= 8.944 cm.