Question

9. In a circle two parallel chords of 48 cm and 288 cm
lengths are 160 cm apart. What is the diameter of circle ?
1. 290 cm
2. 298 cm
3. 328 cm
4. 360 cm
​

Answer 1

$\bold\pink{\fbox{\sf{Solution}}}$

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=21AB=21×14 cm =7 cm and

CQ=21CD=21×48 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=OA2−AP2=252−72 cm =24 cm

Again in ΔOCQ, by Pythagoras theorem, we have

OQ=OC2−CQ2=252−242 cm =7 cm

∴PQ=OP−OQ=(24−7) cm =17 cm

Answer 2

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