Question

The angle bisectors of XYZ intersect at point A, and the perpendicular bisectors intersect at point C. AB_XZ What is the radius of the inscribed circle of XYZ?

Answer 1

r=4.5 units

Explanation:

The incenter is the point forming the center of a circle inscribed in the triangle. It is constructed by taking the intersection of the angle bisectors of the three vertices of the triangle. Therefore, the point A is the incenter of the triangle XYZ.

The radius of the inscribed circle is obtained by dropping a perpendicular from the incenter to any of the triangle legs. Since AB⊥XZ, then AB is the radius of the inscribed circle.

Thus, r=4.5 units.

Answer 2

Very simple.
The inscribed circle will be touching all the three edges of the triangle with its center at point A.
The smallest circle that can be inscribed inside the triangle will be having the radius equal to the length of line segment AB,which is 4.5 units.
I hope it helps.