Question

In a circle of radius 25cm, a chord
is drawn 20cm away from the centre.
find the length of the chord.

Answer 1

Answer:

Given: 'O' is the centre of thee circle.

seg AB is the chord

seg OM is perpendicular to chord AB

seg OM= 20cm

Radius OB= 25cm

To find: length of chord AB

Solution: 1. In right angled triangle OMB,

OB²=OM²+MB²..........By Pythagoras theorem

25²= 20²+MB²

625=400+MB²

625-400=MB²

MB²=225

Taking square root on both sides,

MB= 15cm

2. seg OM is perpendicular to chord AB......given

chord AB= 2×MB........The perpendicular drawn from the centre of the circle to the chord bisects the chord

chord AB= 2×15

chord AB= 30cm