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In the given diagram, the circle touches the y-axis at the point K who

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In the given diagram, the circle touches the y-axis at the point K who  [#permalink]

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New post 30 Jan 2017, 00:07
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In the given diagram, the circle touches the y-axis at the point K whose coordinate is \((0,7)\). If the area of triangle CKO is \(21\) \(units^2\), where C is the center of the circle, find the area of the circle.

    A. \(16π\)
    B. \(21π\)
    C. \(24π\)
    D. \(36π\)
    E. \(49π\)

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In the given diagram, the circle touches the y-axis at the point K who  [#permalink]

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New post Updated on: 05 Feb 2017, 11:21
The official solution has been posted. Looking forward to a healthy discussion..:)
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Originally posted by EgmatQuantExpert on 30 Jan 2017, 00:08.
Last edited by EgmatQuantExpert on 05 Feb 2017, 11:21, edited 1 time in total.
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Re: In the given diagram, the circle touches the y-axis at the point K who  [#permalink]

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New post 30 Jan 2017, 08:08
Area of triangle => 1/2 * 7 *r = 21. This gives radius as 6. Area of circle is 36π
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Re: In the given diagram, the circle touches the y-axis at the point K who  [#permalink]

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New post 30 Jan 2017, 08:17
EgmatQuantExpert wrote:
Image

In the given diagram, the circle touches the y-axis at the point K whose coordinate is \((0,7)\). If the area of triangle CKO is \(21\) \(units^2\), where C is the center of the circle, find the area of the circle.

    A. \(16π\)
    B. \(21π\)
    C. \(24π\)
    D. \(36π\)
    E. \(49π\)



Please refer the below attached fig.
As a tangent always makes 90 Deg with centre.
thus the triangle has height = 7 and base =radius = x (let)
given area=21units^2
area = 1/2*base *height
1/2*7*x=21
x=6
thus area of circle = pi* radius^2
= pi*6^2
36π

Ans D
Attachments

33-e1485759861769.jpg
33-e1485759861769.jpg [ 13.2 KiB | Viewed 1266 times ]

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Re: In the given diagram, the circle touches the y-axis at the point K who  [#permalink]

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New post 05 Feb 2017, 11:21
Hey,

PFB the official solution. :)

Given:

    • The circle touches the y-axis at a point \(K (0,7)\).
    • The area of triangle CKO is \(21 units^2\),

Find:

    • We need to find the area of the circle.

Approach and Working:

    • We are given that
      o The circle touches the y-axis at a point \(K (0,7).\)
    • And we are asked to find what is the area of the circle.
    • We know that the area of the circle can be written as
      o \(Area =\) \(πr^2\)
      o Where \(r\) is the radius of the circle.
    • Thus, we can conclude that to find the area of the circle, we need to find the value of the radius of the circle.
    • We are given
      o The area of triangle CKO is \(21 units^2\), where C is the centre of the circle.
    • If we mark the centre C and join O, we get the triangle CKO as shown in the figure.
Image
    • From the diagram, it is clear that the radius of the circle is r units.
    • And since we know that the area of the triangle is \(21 units^2\), we can write
      o \(\frac{1}{2}* 7 * r = 21\)
      o \(r = 6\) units.
    • Now that we have the radius, we can easily find the area of the circle which is
      o Area of the circle = \(πr^2\) = \(π * 62\) = \(36π\) \(units^2\)
    • The correct answer choice is Option D.

Thanks,
Saquib
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Re: In the given diagram, the circle touches the y-axis at the point K who  [#permalink]

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