Question

Two parallel chords lie on opposite sides of the Centre of a circle of radius 13cm. Their lengths are 10cm and 24cm what is the distance between the chords

Answer 1

Step-by-step explanation:

Let the diameter be AOB = 26 cm(r = 13 cm), 2 parallel chords be CD = 10 cm and EF = 24 cm.

From centre O to the chords draw a perpendicular and a radius, the chord will be half the length ie CD/2 = 5 cm and EF/2 = 12 cm.

Using Pythagoras’ Theorem, OC^2 = (CD/2)^2 + perpendicular^2 and OF^2 = (EF/2)^2 + perpendicular^2 => 13^2 = 5^2 + perpendicular^2 and 13^2 = 12^2 + perpendicular^2.

13^2 = 5^2 + perpendicular^2 => perpendicular = sqrt(169 - 25) = 12 cm.

13^2 = 12^2 + perpendicular^2 => perpendicular = sqrt(169 - 144) = 5 cm.

Distance between chords = 12 + 5 = 17 cm.