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Question
AB and CD are two parallel chords of a circle with centre O such that AB = 6 cm and CD= 12 cm. The chords are on the same side of the centre and the distance between them is 3 cm. The radius of the circle is
Options
6 cm
- \[5\sqrt{2} cm\]
7 cm
- \[3\sqrt{5} cm\]
Solution
We have to find the radius of the following circle:
In triangle OND,
`x^2 + 36 = r^2` …… (1)
Now, in triangle AOM,
`r^2 = 9 + (x +3)^2` …… (2)
From (1) and (2), we have,
`r^2 = 9 + (sqrtr^2 - 36 + 3)^2`
`⇒ r^2 = 9 + r^2 - 36 + 9 + 6 sqrt(r^2 - 36 )`
`⇒ 3 = sqrt(r^2 - 36)`
`⇒9 = r^2 - 36`
`⇒r^2 = 45 ⇒ r =3sqrt(5)`
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