Question

in a circle of radius 5cm,AB and CD are two parallel chords of length 8cm and 6 cm respectively calculate the distance between the chords if they are on the same side of centre

Answer 1

The distance between the chords is 1cm. It's a
long question plz.. mark it as brainliest question.!!!!

Answer 2

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.

$AE=\frac{1}{2}AB=\frac{1}{2}\times 8=4 cm$

$CF=\frac{1}{2}CD=\frac{1}{2}\times 6=3 cm$

In ΔOAE, by Pythagoras theorem

$AO^2=OE^2+AE^2$

$5^2=OE^2+4^2$

$OE^2=25-16=9$

$OE=3 cm$

In ΔOCF, by Pythagoras theorem

$CO^2=OF^2+CF^2$

$5^2=OF^2+3^2$

$OF^2=25-9=16$

$OF=4 cm$

The distance between the chords is

$CF=OF-OE=4-3=1 cm$

Hence, the distance between two chords is 1 cm