Two parallel lines touch the circle at points A and B respectively. If area of the circle
is 25π cm

,then AB is equal to
(a) 5 cm (b) 8 cm (c) 10 cm (d) 25 cm

Answer :

we form our diagram , As :

Here tangent PQ  | | RS , And PQ touch circle at  "  A "  and RS touches the circle at "  B " .

we know " A tangent to a circle is perpendicular to the radius at the point of tangency. "

So,

$\angle$ PAO = 90$°$ ,

$\angle$ QAO = 90$°$

And

$\angle$ RBO = 90$°$ ,

$\angle$ SBO = 90$°$

And

$\angle$ QAO + $\angle$ RBO = 180$°$

And  we know angle on same side of transversal line is also 180$°$ .

So, we can say that AB is diameter of circle  .

Given Area of circle  =  25$\mathrm{\pi }$

We know Area of circle  =  $\mathrm{\pi }$ r²  , So

  $\mathrm{\pi }$ r²  =  25$\mathrm{\pi }$

r² =  25

r  =  5 
So,
Diameter AB  =  10 cm