Question

A triangle has a 60° angle, and the two adjacent sides are 12 and "12 times the square root of 3". Find the radius of a circle with the same vertex as a center, if the arc in the triangle bisects the area of the triangle.

Answer 1

Answer:

r = 10.91 units.

Step-by-step explanation:

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 = $\frac{1}{2} \times 12 \times 12\sqrt{3} \times \sin 60^{\circ} = 108$ 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  

$\pi r^{2} \times \frac{60}{360} = \frac{108}{2}$

⇒ 0.5238 r² = 54

⇒ r² = 103.092

⇒ r = 10.15 units. (Answer)