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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
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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, 09:44
00:00

Difficulty:

45% (medium)

Question Stats:

55% (01:39) correct 45% (01:36) wrong based on 20 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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Joined: 09 Mar 2018
Posts: 1000
Location: India
Re: A triangle is inscribed in a circle, whose diameter is one of the side  [#permalink]

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03 Feb 2019, 10:07
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, 10:18
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
Attachment:

atul-chandan-200782-6.jpg [ 7.29 KiB | Viewed 151 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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Abhishek....

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Re: A triangle is inscribed in a circle, whose diameter is one of the side   [#permalink] 03 Feb 2019, 10:18
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