The sides of the triangle are 26, 28 and 30. Point M is remote from the plane of the triangle and is located at the same

The sides of the triangle are 26, 28 and 30. Point M is remote from the plane of the triangle and is located at the same distance from its sides. Find this distance.

Given:
ABC – triangle
AB = 26
BC = 28
AC = 30
Find: Distance of the sides of the triangle.
Decision:
Consider the triangle ABC
MO = 6
О – the center of the inscribed circle, draw the radii perpendicular to the points of tangency
K for AC, D for BC, H for AB
OD = OK = OH = radius
МD = MK = МН (by condition)
Find the semi-perimeter ABC:
p = (AB + BC + AC) / 2 = (26 + 28 + 30) / 2 = 42
Find the area ABC
S = √ (p * (p-AB) * (p-BC) * (p-AC) = √42 * 16 * 14 * 12 = 336
Next, we find the radius using the following formula:
R = S / p = 336/42 = 8 = OK
The IOC triangle is rectangular, it follows that
MK = MO ^ 2 + OK ^ 2 = √36 + 64 = 10