rxs0005 wrote:

If a triangle inscribed in a circle has area 40, what is the area of the circle?

(1) The base of the triangle is equal to the diameter of the circle.

(2) The measure of one of the angles in the triangle is 30.

Given : Area of triangle say ABC with AC as the longest side is 40

DS: Area of circle.

Statement 1 : AC is the diameter of the circle.. So, /_B = 90 deg. And hence 1/2* AB* BC = 40 i.e. AB * BC = 80

NOT SUFFICIENT to find AC /2

Statement 2: Since measure of one angle is 30 . But we don't know about other angles and hence we can't relate it with the area of triangle to find its sides.

NOT SUFFICIENT

Combined : Third angle is 60.

AB*BC = 80 .........................(i)

Also AB/Sin30 = BC/Sin60 or AB/Sin60 = BC/Sin 30 (ii)

By solving (i) and (ii) for Either case we will get value of AB and BC..

Both cases will finally result in same value of AC = \(\sqrt{{AB^2+BC^2}}\)

Then we can find area of circle = pi*AC^2/4

Answer C
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