Incenter and Circumcenter

Point A is the incenter of DEF. What is the value of n?

b. 11

What value of n would make point A the circumcenter?

b. 3

Point G is the i center of the triangle. What is the value of x?

b. 8

Point A is the incenter of DEF. What is the length of NA?

b. 9 units

Point P is the incenter of RST. Which must be true?

b. BP ~= PC

The figure shows a circle circumscribed around a triangle. What is constructed first when creating the circle?

b. perpendicular bisector a of the sides of the triangle.

Point X is the circumcenter of ABC. What is the length of MB?

c. 2.5 cm

Point H is the circumcenter of JKL. Which must be true?

c. JH ~= LH

The figure shows a circle inscribed in a triangle. To construct the inscribed circle, angle bisectors were first constructed at each angle of the triangle. Which happened next?

c. Segments perpendicular to the sides of the triangle through the intersection of the angle bisectors were constructed.

In the diagram, Z is the circumcenter of triangle TUV. What is the length of VZ?

d. 10 units

Point Y is the circumcenter of triangle DEF. Which statement is true about point Y?

d. Point Y is the center of the circle that passes through points D, E, and F.

Point A is the incenter of triangle DEF. Which must be true? Check all that apply.

Point A is the center of the circle that passes through points X, Y, and Z. ZA ~= YA <AEX ~= <AEZ

Point A is the point of concurrency of the angle bisectors of DEF. What is the length of ZA?

a. ZA = 3cm