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?
Answer & explanation
Correct answer: option 3
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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