AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 2 AB.  Both chords are on the same side of the center of the circle.  If the distance between them is equal to one-fourth of the length of CD, then the radius of the circle is?

5\(\sqrt {5}\)

MN = 20 × \(\frac{1}{4}\) = 5

OB = OD = radius of circle,

Let OM = x

Now,

In Δ OBN:⇒ OB² = ON² + NB² = (5 + x)² + 5²

In Δ OMD:⇒ OD² = OM² + MD² = x² + 10²   ..........(i)

Here, OB² = OD²  (because both lines are radius)

⇒ (5 + x)² + 5² = x² + 10²   ⇒ x = 5 = OM

From (i)

⇒ OD² = OM² + MD² = 5² + 10² = 125

⇒ Radius = OD = \(\sqrt {125}\) = 5\(\sqrt {5}\)