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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 03 Jul 2020, 02:46
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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 centre of the circle, find the area of the circle.

A. 16π
B. 21π
C. 24π
D. 36π
E. 49π


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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 03 Jul 2020, 02:57
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Explanation:
Triangle CKO will be right angle triangle.
With Base as CK (which also radius of circle), Height as KO = 7
Area of Triangle = 21
1/2 x B X H = 21
1/2 x B x 7 =21
B = 6
Radius 6
Area of circle = πr^2 = 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 03 Jul 2020, 07:23
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IMO-D

Area of triangle is =1/2*b*h
Here height is given=7
Area=21
21=1/2*7*b
B=6
Base is equal to radius of circle

Area of circle =pi r^2
=36 pi

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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 05 Jul 2020, 04:44
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Bunuel wrote:
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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 centre of the circle, find the area of the circle.

A. 16π
B. 21π
C. 24π
D. 36π
E. 49π


Area of triangle =\( \frac{1}{2}*b*h\)

\(21 =\frac{1}{2}* radius * height \)

\(21=\frac{1}{2}*r*7\)

r=6

Area of circle= \(πr^2\) = \(π*6^2\)=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 12 Jul 2020, 20:41
Hi Bunuel,

What does "...area of triangle CKO is 21 units^2" mean? I read 21 units^2 as \(21^2\) and couldn't solve the problem. I got confused by the ^2. Is there any purpose of it, or is it a mistake? Many thanks!
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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 12 Jul 2020, 23:30
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durden700 wrote:
Hi Bunuel,

What does "...area of triangle CKO is 21 units^2" mean? I read 21 units^2 as \(21^2\) and couldn't solve the problem. I got confused by the ^2. Is there any purpose of it, or is it a mistake? Many thanks!


"Unit" there is some measurement of length, and unit^2 is measurement of the area. The same way, for example, as "meter" is a measurement of length, and meter^2 is measurement of the area.
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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 13 Jul 2020, 00:09
Bunuel wrote:
durden700 wrote:
Hi Bunuel,

What does "...area of triangle CKO is 21 units^2" mean? I read 21 units^2 as \(21^2\) and couldn't solve the problem. I got confused by the ^2. Is there any purpose of it, or is it a mistake? Many thanks!


"Unit" there is some measurement of length, and unit^2 is measurement of the area. The same way, for example, as "meter" is a measurement of length, and meter^2 is measurement of the area.


That makes perfect sense. I didn't realize it. Of course - it's squared as it refers to the area. \(Unit * unit = unit^2\). :facepalm_man: Thanks!
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Re: In the given diagram, the circle touches the y-axis at the point K who   [#permalink] 13 Jul 2020, 00:09

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

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