Question

in a circle of radius 5 cm, AB and CD are two parallel chords of length 8 cm and 6 cm respectively. Calculate the distance between the chords if they are (i) on the same side of centre (ii) on opposite side of the centre.​

Answer 1

Answer:

Step-by-step explanation:

Two chords AB and CD of a circle with centre O and radius OA or OC

OA=OC=5cm

AB=8cm

CD=6cm

OM and ON are perpendicular from O to AB and CD respectively.

M and N are the mid-points of AB and CD respectively

In figure (i) chord are on the same side

And in figure (ii) chord are on the opposite

Sides of the centre

In right △OAM

OA

2

=AM

2

+OM

2

(By Pythagoras Axiom)

(5)

2

=(4)

2

+OM

2

(AM=1/2AB)

25=16+OM

2

OM

2

=25−16=9=(3)

2

OM=3cm

Again in right △OCN

OC

2

=CN

2

+ON

2

(5)

2

=(3)

2

+ON

2

(CN=1/2CD)

25=9+ON

2

ON

2

=25−9=16=(4)

2

OM=4

In fig. (i), distance MN=ON−OM

=4−3=1cm.

In fig. (ii)

MN=OM+ON=3+4=7cm

Answer 2

$\color{green}{•••Answer•••} \\ \color{green}{•••hope \: it \: helps \: you•••}$