Question

Chord AB of a circle is at a distance of 6m from the centre O of a circle having radius 6m less than the length of the chordAB, then the radius of this circle is____ *

•16 cm

•16 m

•10 m

•10 cm​

Answer 1

Answer:

16 cm

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.