Question

In a circle of radius 6cm, calculate to one significant figure the length of a chord which is 4cm from the center of the circle

Answer 1

Step-by-step explanation:

Let C =4 cm, Chord AB =6 cm

∵OC⊥AB⇒bisectsAB

⇒AC=CB=3cm

∴InOCA,OA

2

+AC

2

(PythagorasTheorem)

=4

2

+3

2

=16+9=25

⇒OA=5cm

Let EF be the chord at a distance of 3cm from the centre.

GIven, radius=OE =5 cm

∴In△OGE,EG

2

=OE

2

−OG

2

=5

2

−3

2

=25−9=16

⇒EG=4cm

∴EF=2×EG=8cm

(Line from centre ⊥ to chord bisects the chord )