Math, asked by yurwish, 6 months ago

In a circle with centre O and radius 5cm, AB and CD are two parallel chords on the same side of centre. if AB=6cm and CD=8cm. find the difference of AB and CD from the centre.​

Answers

Answered by rahulsn07
0

Answer:

Given- A B=6 cm and CD=8 cm are the chords of a circle of radius 5 cm with centre at O.

OP⊥AB at M and OQ⊥CD at N.

To find out - the length of P Q=?

Solution-

We join OC and O A.

So, OC=O A=5 cm, since OC and O A are radii.

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

Now A P=

2

1

A B=

2

1

×6 cm =3 cm and C Q=

2

1

CD=

2

1

×8 cm =4 cm, since the perpendicular from the centre of a circle to a chord bisects the latter.

So, in ΔOAP, by Pythagoras theorem, we have

O P=

O A

2

−A P

2

=

5

2

−4

2

cm =3 cm

Again in ΔOCQ, by Pythagoras theorem, we have

The Q=

OC

2

−C Q

2

=

5

2

−3

2

cm =4 cm.

∴P Q=O P−The Q=(4−3) cm =1 cm

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