Question

what is the length of chord which is at a distance of 4 cm from the centre of a circle of radius 5cm?​

Answer 1

The chord of a circle (PQ)=?

distance of the chord from the centre(OR)=4cm

radius of the circle(OP)=5cm

By Pythagoras theorem,

OPsq.=OR sq.+PR sq.

5sq.=4 sq.+PR sq.

25 =16 +PR. sq.

PR sq.=25-16

PR sq. =9cm

therefore PR=3cm

PR +QR=3+3= 6cm(the perpendicular drawn from centre to chord bisects the chord.

therefore length of the chord is 6 cm