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?
Answer & explanation
Correct answer: option 4
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\(\sqrt {5}\)