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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 Same Side of the Centre and Distance Between Them is 3 Cm. the Radius of the Circle is - Mathematics

MCQ

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

  • \[3\sqrt{5} cm\]

     

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Solution

\[3\sqrt{5}cm\]
Let distance between the centre and the chord CD be x cm and the radius of the circle is r cm.
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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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 15 Circles
Q 28 | Page 112
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