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If P is the center of the circle shown above, and BAC=30º, and the are

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If P is the center of the circle shown above, and BAC=30º, and the are  [#permalink]

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New post Updated on: 09 May 2015, 04:03
1
3
00:00
A
B
C
D
E

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  45% (medium)

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68% (02:30) correct 32% (02:19) wrong based on 73 sessions

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If P is the center of the circle shown above, and BAC=30º, and the area of triangle ABC is √3, what is the radius of the circle?

A. 1/2
B. 1/(√2)
C. 1
D. √2
E. 2

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Originally posted by reto on 09 May 2015, 01:59.
Last edited by Bunuel on 09 May 2015, 04:03, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If P is the center of the circle shown above, and BAC=30º, and the are  [#permalink]

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New post 09 May 2015, 03:01
1
1
Triangle inscribed in a semicircle is always a right triangle. See attached figure
ABC = 90º.
Since BAC = 30º this is a 30-60-90 triangle so the sides are in the ratio x: x√3:2x
Area = 0.5*x*x√3 = √3
x = √2 ; (Since 2x = 2r; x = r)
So radius = √2

Answer D

Ambarish
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Re: If P is the center of the circle shown above, and BAC=30º, and the are  [#permalink]

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New post 27 Jul 2016, 23:20
triangle is 30, 60, 90 and sides will be x , sq root(3) x, and 2x respectively
then 1/2 * x* sq root(3) x= sq root(3)
x = sq root(2)
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Re: If P is the center of the circle shown above, and BAC=30º, and the are  [#permalink]

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Re: If P is the center of the circle shown above, and BAC=30º, and the are   [#permalink] 14 Apr 2019, 12:40
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