$\triangle ABC$ is an equilateral triangle inscribed in a circle of radius $r$. What is the area of the largest square that can be inscribed inside it?
My doubt: How side of an equilateral triangle will be $r\sqrt{ 3}$
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Sign up to join this community$\triangle ABC$ is an equilateral triangle inscribed in a circle of radius $r$. What is the area of the largest square that can be inscribed inside it?
My doubt: How side of an equilateral triangle will be $r\sqrt{ 3}$
$\angle OBC = 30^\circ$, Hence $BM=r\cos 30^\circ = \frac{\sqrt3 r}{2}.$
Task given to you, find the length of $BC$.
Hint: Draw the radii from the center of the circle to the vertices of the triangle. Do you notice anything special about the resulting three smaller triangles? What are their angles?