If you have a square inscribed within a circle, you can split the square into two 45-45-90 triangles using the diameter, but how would you write the perimeter of this square as a function of the diameter?
Write the perimeter of a square inscribed in a circle as a function of the diameter?
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algebra-precalculus
1 Answers
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Let's call $c$ the side length of the square. Then by the Pythagorean theorem:
$$c^2+c^2=d^2$$
where $d$ is the diameter of the circle.
Thus:
$$c=\frac{d}{\sqrt{2}}$$
And the perimeter of the square is:
$$4c=\frac{4d}{\sqrt{2}}=2\sqrt{2}d$$