Question

In the figure
figure o'is the centre
of the circle A B = 12cm
CD 2 1 6cm
om = 8cm, then
length of MN is?​

Answer 1

Answer:

Given- AB=16 cm and CD=14 cm are the chordsof a circle with centre at O.

OM(=6 cm)⊥AB at M and ON⊥CD at N.

To find out -  

If the length of ON=  

m

​  

 cm, then m=?  

Solution-

We join OCand OA.

ΔOAM and ΔOCN are right ones, since OM⊥AB at M and ON⊥CD at N.  

Now AM=  

2

1

​  

AB=  

2

1

​  

×16 cm =8 cm and CN=  

2

1

​  

CD=  

2

1

​  

×14 cm =7 cm since the perpendicular from the centre of a circle to a chord bisects the latter.

So, in ΔOAM, by Pythagoras theorem, we have

OA=  

OM  

2

+AM  

2

 

​  

=  

6  

2

+8  

2

 

​  

 cm =10 cm and it\ is the radius of the circle.

∴OC=OA=10 cm.  

Again in ΔOCN, by Pythagoras theorem, we have

ON=  

OC  

2

−CN  

2

 

​  

=  

10  

2

−7  

2

 

​  

 cm =  

51

​  

 cm  

But given that ON=  

m

​  

.

∴ m=51cm  

2

Explanation:

Answer 2

Explanation:

the above anwer is correct