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

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

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New post 03 Feb 2019, 10:44
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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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New post 03 Feb 2019, 11:07
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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



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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New post 03 Feb 2019, 11:18
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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
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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New post 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.

Answer 1:π, Option C

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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