Question

Radius of circle with centre o is 25 cm. Find the distance of a chord from the centre if the lengthof chord is 48 cm.

Answer 1

What is the length of a chord if the radius is 25 cm and the distance between the midpoint of the chord to the centre of a circle is 7 cm?

First, sketch it.

You find a right-angle triangle with hypotenuse 25 (the radius) and one side 7 (the altitude) and the unknown 3rd side

Pythagoras:

7² + x² = 25²

x² = 625 - 49 =576

x = 24

The chord is 48cm

(You may recognise the 7–24–25 Pythagorean Triplet, like 3–4–5 and 5–12–13)

Answer 2

$\sqrt{625 - 576} = \sqrt{49} = 7$