Find the radius of a circle circumscribed about a triangle MNP if MN = 5, NP = 16, NA = 4, NA is the height of the MNP triangle

The solution of the problem:

1. Let’s define the third side of the triangle МР.

MP = MA + AP;

MA ^ 2 = MN ^ 2 – NA ^ 2 = 5 ^ 2 – 4 ^ 2 = 25 – 16 = 9;

NA = √9 = 3.

AP ^ 2 = NP ^ 2 – NA ^ 2 = 26 ^ 2 – 4 ^ 2 = 240;

AP = √240 = 15.5;

MР = 15.5 + 3 = 18.5.

2. Determine the area of the triangle.

S = 1/2 MP * NA;

S = ½ * 18.5 * 4 = 37.

3. Determine the radius of the circle circumscribed about the triangle.

R = MN * NP * MP / 4S;

R = 5 * 16 * 18.5 / 4 * 37 = 1480/148 = 10

Answer: The radius of the circle is 10.