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

a. Construct the perpendicular bisector of segment XY.

b. Construct a line parallel to segment YZ.

c. Construct a copy of angle X.

d. Construct the angle bisector of angle Y.

2, Aaron is constructing a circle circumscribed about a triangle. He has partially completed the construction, as shown below. What should be his next step in the construction? (Triangle DEF is shown with two sets of intersecting arc markings on either side of side EF. A line segment is drawn through each set of intersecting arc markings and through side EF.)

a. Connect the arc markings to angle E to find another bisector.

b. Use the compass to find the perpendicular bisector for side DF.

c. Connect three arc markings to the vertices from the triangle.

d. Use the intersection of the arcs to determine the center of the circle.

3, This is a cross-sectional view of candy bar ABC. A candy company wants to create cylindrical container for candy bar ABC so that it is circumscribed about the candy bar. IfAD= 2.5 cm, what is the smallest diameter of wrapper that will fit the candy bar?

(ABC in which point E is between points A and B, point D is between points A and C, point F is between points B and C, segments AE and EB are congruent, segmentsBF and FC are congruent, and angles AED, ABF, and DFC are right angles.)

a.3 cm

b.4 cm

c.5 cm

d.6 cm

4, Quadrilateral CDEF is inscribed in circle A. If the mC = 7x + 11 and mE = 6x, what is the measure of E?

a. 78

b. 85

c. 95

d. 102

5, Apex Grocery wants to build a warehouse that is equidistant from its three stores L, M, and N. Which construction correctly finds the best location of the warehouse?

(Construction X is triangle LMN with an inscribed circle. Point A is on segment LM, point D is on segment MN, and point B is on segment LN, segment AN bisects angle N, segment MN bisects angle M, the angle formed by MDL is a right angle, and point C is the intersection of segments MB, LD, and AN.)

(Construction Y is triangle LMN within a circumscribed circle. Point A is on segment LM, point B is on segment MN, point D is on segment MB, point C is on segment LN, angle MAB is a right angle, angle NCD is a right angle, and point E is the intersection of segments AB and EC.)

a.Construction Y because point E is the incenter of LMN

b.Construction X because point C is the incenter of LMN

c.Construction Y because point E is the circumcenter of LMN

d.Construction X because point C is the circumcenter of the LMN

6, Noah is baking a two-layer cake, in which the bottom layer is a circle and the top layer is a triangle. IfAB= 5 inches andABAC, what does Noah know about the top layer of his cake? (Circumscribed circle D around triangle ABC, arcs AB and AC are congruent.)

a.AB is twice the length ofACbecause their arcs are congruent; therefore, ABC is an isosceles triangle.

b.AB is twice the length ofACbecause their arcs are congruent; therefore, ABC is an equilateral triangle.

c. ABACbecause their arcs are congruent; therefore, ABC is an isosceles triangle.

d.ABACbecause their arcs are congruent; therefore, ABC is an equilateral triangle.

7, Quadrilateral CDEF is inscribed in circle A. Which statements complete the proof to show that CFE and CDE are supplementary? (Quadrilateral CDEF is inscribed in circle A.)

Quadrilateral CDEF is inscribed in circle A, so mCDE+ mCFE= 360. CFE and CDE are _________________, which means that their measures arethe measure of their intercepted arcs. So, mCDE = 2 mCFE andCFE= 2 mCDE. Using the _________________, 2 mCFE + 2 mCDE = 360. Using the division property of equality, divide both sides of the equation by 2, resulting in mCFE + mCDE = 180. Therefore, CFE and CDE are supplementary.

a. inscribed angles; substitution property of equality

b. central angles; substitution property of equality

c. inscribed angles; addition property of equality

d. central angles; addition property of equality

8, Point D is the incenter of triangle BCA. If mFDG = 136, what is the measure of FHG?

(Triangle BCA with inscribed circle D. Segments BF and BH, CF and CG, and AG and GH are tangent to circle D; segments FD, GD, FH, and GH are created from points F, G, D, and H.)

a. 68

b. 44

c. 136

d. 88

9, In BCA, BA = 17 cm, BF = 6 cm, CG = 9 cm. Find the perimeter of BCA.

(Triangle BCA with inscribed circle D. Segments BF and BH, CF and CG, and AG and GH are tangent to circle D.)

a. 32 cm

b. 35 cm

c. 47 cm

d. 52 cm

10, A company is replacing cables with fiber optic lines in rectangular casing BCDE. IfDE= 3 cm andBE= 3 cm, what is the smallest diameter of pipe that will fit the fiber optic line? Round your answer to the nearest hundredth. (quadrilateral BCDE inscribed within circle A)

a. 3.54 cm

b. 3.91 cm

c. 4.24 cm

d. 4.95 cm