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# A triangle is inscribed in a circle, whose diameter is one of the side

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Joined: 25 Dec 2018
Posts: 145
Location: India
GMAT 1: 490 Q47 V13
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A triangle is inscribed in a circle, whose diameter is one of the side  [#permalink]

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03 Feb 2019, 10:44
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45% (medium)

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63% (02:01) correct 37% (01:57) wrong based on 43 sessions

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A triangle is inscribed in a circle, whose diameter is one of the sides of triangle. If the triangle is an isosceles triangle, what is the area of triangle to that of circle?

A. π:1
B. 2π:1
C. 1:π
D. 2:π
E. 1:2π
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Re: A triangle is inscribed in a circle, whose diameter is one of the side  [#permalink]

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03 Feb 2019, 11:07
1
akurathi12 wrote:
A triangle is inscribed in a circle, whose diameter is one of the sides of triangle. If the triangle is an isosceles triangle, what is the area of triangle to that of circle?

A. π:1
B. 2π:1
C. 1:π
D. 2:π
E. 1:2π

A triangle formed using the diameter will have an angle of $$90^o$$ subtended on the circle.

Let diameter = 4, radius = 2, Area of circle = 4π

Area of triangle = 1/2 * 2 root2 * 2 root2 = 4

Ratio = 1:π

C
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Re: A triangle is inscribed in a circle, whose diameter is one of the side  [#permalink]

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03 Feb 2019, 11:18
1
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akurathi12 wrote:
A triangle is inscribed in a circle, whose diameter is one of the sides of triangle. If the triangle is an isosceles triangle, what is the area of triangle to that of circle?

A. π:1
B. 2π:1
C. 1:π
D. 2:π
E. 1:2π
Attachment:

atul-chandan-200782-6.jpg [ 7.29 KiB | Viewed 764 times ]

Here R = h

So, Area of the Triangle is $$\frac{1}{2}*R*2R =R^2$$

Area of the CIrcle is $$πR^2$$

So, Ratio of Area of Triangle to the Area of the Circle is $$R^2 : πR^2 = 1:π$$, Answer must be (C)
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Re: A triangle is inscribed in a circle, whose diameter is one of the side  [#permalink]

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05 Mar 2019, 21:56
1
akurathi12 wrote:
A triangle is inscribed in a circle, whose diameter is one of the sides of triangle. If the triangle is an isosceles triangle, what is the area of triangle to that of circle?

A. π:1
B. 2π:1
C. 1:π
D. 2:π
E. 1:2π

Assuming that the question is asking for the " ratio" of area of triangle to the area of circle.

A triangle in a circle whose one side is the Diameter of a circle is a right angled triangle. With the Hypotenuse of the Triangle = Diameter of the circle.
Further this is an isosceles right angled triangle.

let the sides of the triangle be $$x:x:x\sqrt{2}$$
so Diameter of circle is $$x\sqrt{2}$$
Now we can find the radius and area of the circle . In terms if x.

P.S. The word ratio seems to be missing from the question.
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Re: A triangle is inscribed in a circle, whose diameter is one of the side   [#permalink] 05 Mar 2019, 21:56
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