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19 Sep 2014, 20:13
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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45%
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66% (02:08) correct
34%
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Right triangle DEF has angles in the ratio 1:2:3 and is inscribed in a circle with center C such that each vertex of DEF lies on the circumference of C. If the shortest side of DEF has length x, which of the following represents the area of circle C?
A. 2πx
B. πx^2
C. sq. root 3πx^2
D. 2πx^2
E. 4 πx^2
A. 2πx
B. πx^2
C. sq. root 3πx^2
D. 2πx^2
E. 4 πx^2
20 Sep 2014, 12:53
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neeti1813
The triangle has angles in the ratio 1:2:3 --> a + 2a + 3a = 180° --> a = 30°. So, we have 30-60-90 right triangle.
This is one of the 'standard' triangles you should be able to recognize on sight. A fact you should commit to memory is: the sides are always in the ratio \(1 : \sqrt{3}: 2\).
Since the shortest side is x, then the sides are \(x : \sqrt{3}x: 2x\).
Next, a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle (the reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle).
So, the largest side, the hypotenuse, 2x, must be the diameter of the circle --> radius = x --> \(area = \pi{r^2}=\pi{x^2}\).
Answer: B.,
Hope it's clear.
06 Sep 2017, 22:57
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