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

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Joined: 04 Jan 2015
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In the given diagram, the circle touches the y-axis at the point K who  [#permalink]

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29 Jan 2017, 23:07
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5% (low)

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94% (01:41) correct 6% (02:01) wrong based on 115 sessions

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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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Updated on: 05 Feb 2017, 10:21
The official solution has been posted. Looking forward to a healthy discussion..
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Originally posted by EgmatQuantExpert on 29 Jan 2017, 23:08.
Last edited by EgmatQuantExpert on 05 Feb 2017, 10:21, 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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30 Jan 2017, 07:08
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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30 Jan 2017, 07:17
EgmatQuantExpert wrote:

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 [ 13.2 KiB | Viewed 1390 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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05 Feb 2017, 10:21
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.

• 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
Quant Expert
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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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Re: In the given diagram, the circle touches the y-axis at the point K who &nbs [#permalink] 23 Sep 2018, 06:31
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# In the given diagram, the circle touches the y-axis at the point K who

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