A circle is inscribed in a regular triangle (a3 = 3√3), and a square is inscribed in it. Find the sides of the square.
| August 8, 2021 | education
Determine the radius of a circle inscribed in an equilateral triangle.
R = a / 2 * √3, where a is the side of a regular triangle.
R = 3 * √3 / 2 * √3 = 3/2 cm.
The diagonal of a square inscribed in a circle is the diameter of this circle, then KP = 2 * R = 2 * 3/2 = 3 cm.
In a right-angled triangle NKР, KP ^ 2 = KH ^ 2 + PH ^ 2 = 2 * KH ^ 2.
KН ^ 2 = KP ^ 2/2 = 9/2.
KH = 3 / √2 = 3 * √2 / 2 cm.
Answer: The side of the square is 3 * √2 / 2 cm.
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