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

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Math Expert
Joined: 02 Sep 2009
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In the given diagram, the circle touches the y-axis at the point K who  [#permalink]

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03 Jul 2020, 02:46
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91% (01:39) correct 9% (02:48) wrong based on 80 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 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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03 Jul 2020, 02:57
1
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
Area of circle = πr^2 = 36π

IMO-D
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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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03 Jul 2020, 07:23
1
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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05 Jul 2020, 04:44
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Bunuel 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 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

IMO D
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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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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!
Math Expert
Joined: 02 Sep 2009
Posts: 65829
Re: In the given diagram, the circle touches the y-axis at the point K who  [#permalink]

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12 Jul 2020, 23:30
1
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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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. $$Unit * unit = unit^2$$. Thanks!
Re: In the given diagram, the circle touches the y-axis at the point K who   [#permalink] 13 Jul 2020, 00:09