Question

50 POINTS HELP ASAP! A triangle has a 60 angle and the two adjacent sides are 12 and 12 sqrt 3 find the radius of a circle with the same vertex as the center if the arc inside the triangle divides it into two regions of equal area.
r = ???

Answer 1

The triangle has a 60° angle, and the two adjacent sides are 12 and "12 times the square root of 3".  

So, the area of the triangle, Δ =  sq. units.

Now, we have to find the radius of the circle with the same vertex as a center, if the arc in the triangle bisects the area of the triangle.

So, if the radius of the circle is r units, then  

⇒ 0.5238 r² = 54

⇒ r² = 103.092

⇒ r = 10.15 units. (Answer)