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# What is the area of the triangle inscribed within the circle as shown

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
What is the area of the triangle inscribed within the circle as shown  [#permalink]

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11 Sep 2018, 02:34
00:00

Difficulty:

25% (medium)

Question Stats:

75% (00:49) correct 25% (00:39) wrong based on 28 sessions

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What is the area of the triangle inscribed within the circle as shown above?

(1) The triangle is equilateral.
(2) The radius of the circle is 5.

Attachment:

image004.jpg [ 3.98 KiB | Viewed 481 times ]

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Re: What is the area of the triangle inscribed within the circle as shown  [#permalink]

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11 Sep 2018, 06:11
Bunuel wrote:

What is the area of the triangle inscribed within the circle as shown above?

(1) The triangle is equilateral.
(2) The radius of the circle is 5.

Attachment:
image004.jpg

Statement 1: The triangle is equilateral.
but we dont have any of the dimensions.
Insufficient.

Statement 2: The radius of the circle is 5.
We need to know the angles of the triangle to calculate the area.
Insufficient.

Combining Statements 1 and 2:
Sufficient.

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What is the area of the triangle inscribed within the circle as shown  [#permalink]

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12 Sep 2018, 05:21
1
Bunuel wrote:

What is the area of the triangle inscribed within the circle as shown above?

(1) The triangle is equilateral.
(2) The radius of the circle is 5.

Attachment:
image004.jpg

Question : What is the area of the triangle inscribed within the circle as shown above?

To calculate the area of triangle we need to know
1) Property of triangle whether it's equilateral isosceles, right angle etc.

Statement 1: The triangle is equilateral.

Now we know the type of triangle it is but we have no dimension to calculate the area/side of the triangle hence

NOT SUFFICIENT

Statement 2: Radius of the circle = 5

We know th eradius but we don't know the type of triangle it is hence

NOT SUFFICIENT

Combining the two statements

Radius = 5, i.e.if side of equilateral triangle =a
$$(2/3)*Height-of-equilateral triangle = Radius-of-circle$$
$$(2/3)*(√3/2)a = 5$$
Now, a can be calculated hence

SUFFICIENT

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What is the area of the triangle inscribed within the circle as shown   [#permalink] 12 Sep 2018, 05:21
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