AB and CD are two chords of a circle, such that AB=6 cm, CD =12 cm and AB||CD. If the distance between AB and CD is 3 cm, find the radius of the circle.AB and CD are two chords of a circle, such that AB=6 cm, CD =12 cm and AB||CD. If the distance between AB and CD is 3 cm, find the radius of the circle.
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Step-by-step explanation:given
AB = 6cm, CD = 12 cm
let centre of circle be o.
in triangle AOE,
(r × r) = (6 ×6 )+( x× x)
r^2 = 36 + x^2
( because CD /2 = 12/2 )
~ in triangle COF.
r^2 = 9 + x^2 +9 +6x
= 18 + x^2 + 6x
from eqn 1 and 2
36 +x^2 = 18 +x^2 +6x
36-18 = 6x
18= 6x
x = 3
put value in eqn 1
r^2 = 36+ 9
r = underoot 45
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