Question

The distance between two points A and B is 6 cm. A circle of radius 5 cm is drawn to pass through the points A and B. Find the distance of AB from the centre of the circle.

Answer 1

Answer:

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Step-by-step explanation:

Given- AB is a chord of a circle with centre O.

ON is the perpendicular from O to AB at N.  

ON=6 cm, AB=(OA+6) cm,ON⊥AB  

To find out- the length of the radius of the circle =?

Solution-

Let OA=x−6 cm i.e. AB=x cm.

∴AN=  

2

1

​  

AB=  

2

x

​  

 cm, since the perpendicular from the centre of a circle to a chord bisects the lattar.

Now in ΔOAN, we have

∠ANO=90  

o

 as ON⊥AB.  

So, ΔOAN is a right one with OA as hypotenuse.

∴ applying pythagoras theorem, we have

OA= radius of the given circle =  

ON  

2

+AN  

2

 

​  

=  

6  

2

+AN  

2

 

​  

 

⇒x−6=  

6  

2

+(  

2

x

​  

)  

2

 

​  

 

⇒x(3x−48)=0

⇒x=(0,16) cm

We reject x=0, since it is\quad a finite length.  

So, x=AB=16 cm.