Answer:
The radius of the circle is 14.4 cm.
Step-by-step explanation:
Let a be the side of the equilateral triangle and r be the radius.
The area of a triangle is given by
[tex]A=\frac{1}{2}\cdot a\cdot h\\\\270.633=\frac{1}{2}\cdot a\cdot 21.65\\\\a=25.0007[/tex]
We have calculate the side of the triangle. From the figure,
[tex]BD=\frac{a}{2}\\\\BD=\frac{25.0007}{2}\\\\BD=12.50035[/tex]
Hence, in triangle OBD, we have
[tex]\cos30^{\circ}=\frac{BD}{r}\\\\\frac{\sqrt3}{2}=\frac{12.50035}{r}\\\\r=14.4[/tex]
The radius of the circle is 14.4 cm.
