Question

In a circle with centre O, then length of a diameter is 20cm and AB is a chord of a circle at a distance 6 cm from centre, then AB = ? ​

Answer 1

Answer:Given,

Diameter of the circle = 20 cm

Radius of the circle = 20/2 = 10 cm

distance of chord from the centre = 6 cm

To find,

Length of the chord

In the figure (refer to the attachment)

Using pythagoras theorem in ▲OAM

AM ^2=OA^2 - OM^2

AM^ 2 =10^ 2 -6^ 2 =100-36

AM^ 2 =84

AM=9.2

Using the theorem: A perpendicular drawn from the center of the circle to a chord bisects the chord. i.e, (AM=BM)so,

AB=2c, AM=2×9.2=18.4 cm