The value of x for the circumscribed triangle is equal to 6 using length equidistant from the circumcenter N.
The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. This point is equidistant from the three vertices of the triangle and is the center of the circumcircle, which is the circle passing through all three vertices of the triangle.
Considering the right triangle NHC, the value of x for radius NH and length HC can be derived using Pythagoras rule as follows:
(x - 1)² + (x + 6)² = 13²
x² - 2x + 1 + x² + 12x + 36 = 169
2x² + 10x + 37 = 169
2x² + 10x - 132 = 0
{divide through by 2;
x² + 5x - 66 = 0
factorize by grouping;
x² + 11x - 6x - 66 = 0
x(x + 11) -6(x + 11) = 0
(x - 6)(x + 11) = 0
x = 6 or x = -11
Therefore, we say that the value of x for the circumscribed triangle is equal to 6
Complete question:
Find the value of x for the circumscribed triangle ∆ABC with circumcenter N.