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A circle is tangent to the x-axis at 2 and the y-axis at 2. What is th

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Bunuel
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A circle is tangent to the x-axis at 2 and the y-axis at 2. What is th [#permalink] New post   03 Jul 2020, 04:13
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A circle is tangent to the x-axis at 2 and the y-axis at 2. What is the area of the shaded region?

A. Less than 1
B. Between 1 and 3
C. Between 3 and 5
D. Between 5 and 7
E. Greater than 7

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Re: A circle is tangent to the x-axis at 2 and the y-axis at 2. What is th [#permalink] New post   05 Jul 2020, 00:53
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Bunuel wrote:

A circle is tangent to the x-axis at 2 and the y-axis at 2. What is the area of the shaded region?

A. Less than 1
B. Between 1 and 3
C. Between 3 and 5
D. Between 5 and 7
E. Greater than 7



Area of circle = \(πr^2\) = 3.14*4
Area of the quarter of a circle = \(πr^2\)/4= \(\frac{3.14*4}{4}\) =3.14

area of square = 2*2=4

area of shaded region= 4-3.14 = 0.86 < 1

Hence Answer A
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Re: A circle is tangent to the x-axis at 2 and the y-axis at 2. What is th [#permalink] New post   03 Jul 2020, 04:19
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Let's draw two more tangents, so that it form a square of side 4

Since the circle is tangent at point two its radius is 2.
Area of square = Side^2 = 16
Area of circle = πr^2 = 22/7*2*2 = 88/7 = 12.6

Area of shaded portion = (area of square-area of circle)/4
=> (16-12.6)/4
=> 3.4/4
=> less than 1

Answer is A

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A circle is tangent to the x-axis at 2 and the y-axis at 2. What is th [#permalink] New post   03 Jul 2020, 04:26
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A

Less than one

An important result is that the radius from the center of the circle to the point of tangency is perpendicular to the tangent line.

Line from centre to tangents makes 90 degree angle.

Area of shaded region = Area of square - 1/4 Area of circle with radius 2

Comes out to be less than 1
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Re: A circle is tangent to the x-axis at 2 and the y-axis at 2. What is th [#permalink] New post   03 Jul 2020, 04:55
Explanation:

Assume a sqaure with side 2 ,so area = 4
Circle are with radius 2 = πr^2 = 4π /4 (as we need 1/4 th area) : π

So required area = 4 - π = 4-3.14 = 0.86
which less than 1

IMO-A
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Re: A circle is tangent to the x-axis at 2 and the y-axis at 2. What is th [#permalink] New post   03 Jul 2020, 11:00
IMO A

Let draw the square using tangents and radius

Area of square is =2*2=4
Area of circle= Pi r^2
=22*2*2/7
Are of 1/4 circle is = 22*2**2/(7*4)
=3.14
Area of shaded part is=area of square- are of 1/4 circle
=4-3.14
=.86
Answer is less than 1

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Re: A circle is tangent to the x-axis at 2 and the y-axis at 2. What is th [#permalink] New post   20 Sep 2021, 05:53
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Re: A circle is tangent to the x-axis at 2 and the y-axis at 2. What is th [#permalink]
20 Sep 2021, 05:53
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