⁦A point equidistant from the vertices or the sides of a polygon⁩

⁦From the Ukrainian Grade 10 textbook (algebra and calculus with geometry)⁩, §⁦5, item 35⁩ '⁦Perpendicular and slant⁩': ⁦the key problem about an equidistant point⁩.

⁦If a point M is equally far from all vertices of a polygon, its projection onto the polygon⁩'⁦s plane is the centre of the circumscribed circle⁩: ⁦equal slants MA = MB = MC have equal projections OA = OB = OC⁩.

⁦If M is equally far from the lines containing the sides, its projection is the centre of the inscribed circle (by the theorem of three perpendiculars)⁩.

⁦Then work in the right triangle MOA, where MO is the perpendicular, MA the slant and OA the projection⁩: MO = √(MA^٢ − OA^٢).