PQ and RS are two parallel chords of a circle of length 10 cm and 24 cm, respectively, and lie on the same side of the centre O. If the distance between the chords is 7 cm, what is the radius (in cm) of the circle?

13

Let us consider that , OX = a cm

 OX is perpendicular to RS and OY is perpendicular to PQ.

In triangle OXS,

h² = b² + p²

OS² = 12² + a²

In triangle OYQ,

OQ² = OY² + YQ²

= ( a + 7 )² + 5²

{ OS = OQ ( Radius of circle ) }

12² + a² = ( a + 7 )² + 5²

144 + a² = a² + 49 + 14a + 25

14a = 70

a = 5

Now,

OS² = 12² + a²

= 12² + 5² 

= 144 + 25

= 169

OS = 13

So, Radius of circle = 13 cm