$\triangle ABC$ 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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$\begingroup$ Do you know how to solve further if you get $a=r\sqrt 3$? $\endgroup$ – Jaideep Khare Aug 1 '17 at 20:59
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$\begingroup$ Yes @JaideepKhare $\endgroup$ – EmilySekuz Aug 1 '17 at 21:04
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$\angle OBC = 30^\circ$, Hence $BM=r\cos 30^\circ = \frac{\sqrt3 r}{2}.$
Task given to you, find the length of $BC$.
answered Aug 1 '17 at 21:05
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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?
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$\begingroup$ So, do you know anything special about 30-60-90 triangles? (use trigonometry) $\endgroup$ – Legendre Aug 1 '17 at 21:06
