Question

In a circle, a chord of 50 cm bisects a chord of 40 cm. Find the length of the longer segment of the 50 cm chord.

Answer 1

23cm

Explanation:

In the circle below, AB, CD, and EF are the chords of the circle. Chord CD is the diameter of the circle.

= 2√ (142−82)

= 2√ (196 − 64)

= 2√ (132)

= 2 x 11.5

= 23

Answer 2

The length of the longer segment of the 50 cm chord = 40

Explanation:

let the length of the longer segment of the 50 cm chord = x

so, the other segment = 50 - x

A chord of 50 cm bisects a chord of 40 cm

using the Intersecting Chords Theorem

so, x(50-x) = 20 * 20

50x - x² = 400

x² - 50x + 400 = 0

(x - 40)(x - 10) = 0

x = 40 or x = 10

So, the the length of the longer segment of the 50 cm chord = 40