Question

In a circle of radius 8 cm, two chords, AB = 14 cm and CD = 12 cm, are drawn to the same side of the circle. Find the distance between the two chords.

Answer 1

Step-by-step explanation:

Let AB and CD are two parallel chords of a circle having length 6 cm and 8 cm and radius is O.

Let the radius of the circle be r.

Now draw OP perpendicular to AB and OQ perpendicular to CD.

since OP is perpendicular to AB and OQ is perpendicular to CD and AB || CD

From figure, OP = 4 cm.

P, Q are the mid points of AB and CD respectively. [perpendicular from center bisects the chord]

So AP=PB=

2

AB

=

2

6

=3cm

CQ=QD=

2

CD

=

2

8

=4cm

Now in triangle OAP

OA

2

=OP

2

+AP

2

r

2

=16+9

r=

16+9

r=5cm

Answer 2

Step-by-step explanation:

Let AB and CD are two parallel chords of a circle having length 6 cm and 8 cm and radius is O.

Let the radius of the circle be r.

Now draw OP perpendicular to AB and OQ perpendicular to CD.

since OP is perpendicular to AB and OQ is perpendicular to CD and AB || CD

From figure, OP = 4 cm.

P, Q are the mid points of AB and CD respectively. [perpendicular from center bisects the chord]

So AP=PB= 2AB

=26

=3cm

CQ=QD= 2CD

= 28

=4cm

Now in triangle OAP

OA 2=OP 2+AP

r 2=16+9

r= 16+9

r=5cm