the circle in the diagram shown has center l and radii lj lk li, , .which step is included in the construction of this circle?
a find the circumcenter.
b find the intersection point of the three perpendicular bisectors.
c construct the incenter, l, by finding the intersection points of the three angle bisectors.
d construct the three midpoints i, j, and k on the three triangle sides.

C Construct the incenter, L, by finding the intersection points of the three angle bisectors.

Step-by-step explanation:

Given is a diagram.

The circle in the diagram shown has center L and radii LJ LK LI,

From the picture we find that the circle touches the three sides of the triangle.

This implies that the centre is equidistant from the sides of the triangle.

When a point is equidistant from two intersecting rays we know that the point lies on the angle bisector of the angle made by the rays.

Hence here since L is equidistant from the three sides, we find that L lies on the angle bisectors of the three angles and L is the incentre of the triangle.

Hence option C is right.

C Construct the incenter, L, by finding the intersection points of the three angle bisectors.