Which of the following are properties of the incenter of a triangle? choose all that apply.
a. the incenter is where all of the bisectors of the angles of the triangle meet.
b. the incenter of an obtuse triangle lies on the outside of the triangle.
c. the incenter is equidistant from each vertex of the triangle.
d. the incenter of a triangle is always inside it.

(A.) The incenter is where all of the bisectors of the angles of the triangle meet.

(D.) The incenter of a triangle is always inside it.

Step-by-step explanation:

A P E X

step-by-step explanation:

4227473658779875563886538705958641728563470543621287463824132573847969p05749365273847906970680574936214

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.