What is the área of an equilateral triangle inscribed in a circle?
1) the area outside the triangle is 3Π
2) radius of the circle is 6
Answer is D.
length and height of each side of the triangle can be written in terms of r using the Isosceles Triangle from the center of the circle to any two corners of triangle (angles: 120, 30 30)
given this, the area of triangle can be written in terms of r and also we know area of circle in terms of r that is pi*r^2 - so we should assess each option if it is sufficient to identify what r is
if (1) is known r can be calculated, since the area outside the triangle is difference of two figures that can be written in terms of r and subsequently we can calculate the area of the triangle. (1) alone is sufficient
if (2) using r we can calculate the area of triangle since we know length of each side and height in terms of r. (2) alone is sufficient.
Also note that we can answer DS questions without actually solving the question, we just need to prove if the data given in 1/2 are sufficient or not.
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