Question

An equilateral triangle with side of 2√3 is inscribed in a circle. What is the area of one of the sectors formed by the radii to the vertices of the triangle?

A. 2 π sq.in.

B. 1.33 π sq.in.

C. 2.09 π sq.in.

Answer 1

lenth of altitude\[=\sqrt{(2\sqrt{3})^2-(\sqrt{3} )^2 }=\sqrt{12-3}=\sqrt{9}=3\]
we know altitudes bisect in the ratio 2:1
so radius\[=\frac{ 2 }{ 2+1}\times 3=2\]
do you know angle between two radii (of an equilateral triangle)?

Answer 2

\[area ~of~sector~AOB=\frac{ \pi(2)^2 }{3 }=\frac{ 4\pi }{ 3 }=1.33 ~\pi ~sq.in\]
as it is 1/3 of the whole circle whose radius=2 in