Circles with and Without Coordinates

Point O is the center of the circle in the diagram. What is
m∠BCA?

A.
80°

B.
75°

C.
70°

D.
65°

DG and EG are tangent to circle C and circle F. The points of tangency are A, B, D, and E. If m∠DFE = 140°, what is m∠ACB?

A.
160°

B.
140°

C.
120°

D.
110°

In the diagram, point O is the center of the circle and AC and BD intersect at point E. If m∠AOB = 90° and
m∠COD = 16°, what is m∠CED?

A.
37°

B.
48°

C.
53°

D.
62°

Quadrilateral BCDE is inscribed in circle A as shown. BD divides the quadrilateral into two triangles, ∆BCD and ∆BED. Which statement is true about the triangles?

A.
The angle bisectors and the perpendicular bisectors for both triangles intersect at the same point.

B.
The angle bisectors of ∆BCD intersect at the same point as those of ∆BED.

C.
The perpendicular bisectors of ∆BCD intersect at the same point as those of ∆BED.

D.
The angle bisectors of ∆BCD intersect at the same point as the perpendicular bisectors of ∆BED.

The triangle in the diagram represents a mold that Anna uses to shape dough before baking. Anna also has a circular mold whose rim just fits inside the rim of the triangular mold.

The radius of the circular mold is approximately
___ cm.

a. 5.35
b. 9.62
c.. 11.35

In the diagram, P1P2 and Q1Q2 are the perpendicular bisectors AB of and BC , respectively. A1A2 and B1B2 are the angle bisectors of ∠A and ∠B, respectively. What is the center of the circumscribed circle of ∆ABC?

A.
P

B.
Q

C.
R

D.
S

The figure shows an aerial view of a playground. If David runs around the field three times, he covers a distance of
___yards.

What is the area of the shaded region in the diagram? Use the value π = 3.14, and round your answer to two decimal places.

A.
19.23 square units

B.
9.81 square units

C.
1.57 square units

D.
9.42 square units