The sides of the triangle are 26 cm, 28 cm, 30 cm. Point M is not 6 cm from the plane of the triangle and is located

The sides of the triangle are 26 cm, 28 cm, 30 cm. Point M is not 6 cm from the plane of the triangle and is located at the same distance from its sides, find this distance

Triangle ABC, AB = 26, BC = 28, AC = 30, MO = 6, O is the center of the inscribed circle, we draw radii perpendicular to the points of contact, K to AC, D to BC, H to AB, OD = OK = OH = radius, MD = MK = MН by condition, semi-perimeter ABC (p) = (AB + BC + AC) / 2 = (26 + 28 + 30) / 2 = 42,

area ABC = square root of (p * (p – AB) * (p – BC) * (p – AC)) = square root of (42 * 16 * 14 * 12) = 336,

radius = area / semi-perimeter = 336/42 = 8 = OK, triangle MOK is rectangular, MK = (MO squared + OK squared) = root (36 + 64) = 10