Question

What is the first step in constructing an inscribed circle inside triangle XYZ?

Construct the incenter of triangle XYZ.
Construct the circumcenter of triangle XYZ
Construct the centroid of triangle XYZ.
Construct the orthocenter of triangle XYZ.

Answer 1

construct the incenter of triangle XYZ

Step-by-step explanation:

The incenter of a triangle is said to be the point inside a triangle which divides the distances to the sides of the triangle equally, it is formed by the intersection of a triangle's three angles bisectors

from this point we can start to construction of an inscribed circle in the triangle, and this is because the incenter of a triangle is also seen as the center of the circumference.

while the circumcenter of a triangle is the point where the perpendicular bisectors of the triangle intersect. it is also known as the center of the circumcircle of the triangle

Answer 2

Construct the incenter of triangle XYZ.

Step-by-step explanation:

The incenter of a triangle is the point from which the distances to the sides are equal, in this point we can start to construct the inscribed circle in the triangle, because the incenter would also be the center of the circumference.