The value of x that would make P the incenter of the triangle is x = 7.
The value of x that would make P the circumcenter of the triangle is x = 6.
In Mathematics and Euclidean Geometry, the point of concurrency of the angle bisectors is referred to as the incenter of a triangle. Additionally, the incenter is equidistant from the three sides of a triangle.
Based on the diagram shown above, a value of x that would make P the incenter of the triangle can be calculated as follows;
3x + 3 = 24
3x = 24 - 3
3x = 21
x = 21/3
x = 7.
A circumcenter is the point where perpendicular bisectors (right-angled lines to the midpoint) of the sides of a triangle meet together or intersect. In this context, a value of x that would make P the circumcenter of the triangle can be calculated as follows;
5x - 4 = 26
5x = 26 + 4
5x = 30
x = 30/5
x = 6