The apex of a triangle is divided into three arcs, the length of which is 3: 5: 10.

The apex of a triangle is divided into three arcs, the length of which is 3: 5: 10. Find the radius of the circle if the smaller side is 19.

Let’s draw from the center of the circle describing the triangle, the radii to the vertices of the triangle. The central angles formed by the radii will be equal to the angular magnitude of the arcs on which they rest, that is, they also correlate as 3: 5: 10. The arcs form a complete circle, therefore the sum of the angular magnitudes of the arcs AB, BC and CA is 360 degrees. Let us prove that the radii based on the smallest arc form an equilateral triangle with the smallest side.
Answer: 19.