Point K is removed from each side of the regular triangle by 30 cm, and from its plane by 18 cm.

| September 9, 2021 | education

Point K is removed from each side of the regular triangle by 30 cm, and from its plane by 18 cm. Find the length of the radius of the circle inscribed in this triangle, the length of the side of the triangle.

Since the distance from the point K to the sides of the triangle ABC is equal, the point K is projected to the point O, the center of the circle inscribed in the triangle.

Triangle ABC is equilateral, then point O is the intersection point of medians, heights and bisectors.

In a right-angled triangle HOK, according to the Pythagorean theorem, OH ^ 2 = HK ^ 2 – OK ^ 2 = 900 – 324 = 576.

OH = r = 24 cm.

The radius of the inscribed circle in an equilateral triangle is: r = √3 * BC / 6.

BC = r * 6 / √3 = 24 * 6 / √3 = 48 * √3 cm.

Answer: The radius of the inscribed circle is 24 cm, the side of the triangle is 48 * √3 cm.



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