Question

Radius of a circle is 25 cm. There are two chords of length 48 cm each. What will be the distance between the two chords?​

Answer 1

Answer:

Given- AB=14 cm and CD=48 cm are the chords of a circle of radius 25 cm with centre at O.

OP⊥AB at M and OQ⊥CD at N.

To find out -

If the length of PQ=?

Solution-

We join OC and OA.

So, OC=OA=25 cm, since OC and OA are radii

ΔOAP and ΔOCQ are right ones, since OP⊥AB at P and OQ⊥CD at Q.

Now AP=

2

1

AB=

2

1

×14 cm =7 cm and

CQ=

2

1

CD=

2

1

×48 cm =24 cm

Since the perpendicular from the centre of a circle to a chord bisects the latter.

So, in ΔOAP, by Pythagoras theorem, we have

OP=

OA

2

−AP

2

=

25

2

−7

2

cm =24 cm

Again in ΔOCQ, by Pythagoras theorem, we have

OQ=

OC

2

−CQ

2

=

25

2

−24

2

cm =7 cm

∴PQ=OP−OQ=(24−7) cm =17 cm

Hope it helps you :)