Question

In a circle of radius 5 cm , AB and CD are two parallel chords. The distance between the chords is 1 cm and 7 cm when they are on the same and opposite sides of the centre. Find the length of the two chords......


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Answer 1

Answer:

The distance between two chords is 1 cm

Step-by-step explanation:

Given a circle of radius 5 cm, AB and CD are two parallel chords of length 8 cm and 6 cm respectively.

we have to find the distance between the chords if they are on the same side of centre.

By theorem, radius from the centre perpendicularly bisect the chord of circle.

AE = 1/2 AB = 1/2 X 8 = 4 Cm

CF = 1/2 CD = 1/2 X 6 = 3 Cm

In ΔOCF, by Pythagoras theorem

CO^2 = OF^2 + CF^2

5^2 = OF^2 + 3^2

OF^2 = 16

OF = 4 Cm

The distance between the chords is

CF = OF - OE = 4 - 3 =1 Cm

Hence, the distance between two chords is 1 cm.

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