In the diagram below of circle , diameter and chord are drawn, and .
What is ?
A circle with a diameter of 10 cm and a central angle of is drawn below. What is the area, to the nearest tenth of a square centimeter, of the sector formed by the angle?
A circle with a radius of 5 was divided into 24 congruent sectors. The sectors were then rearranged, as shown in the diagram below. To the nearest integer, the value of is
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil.
Triangle is the image of triangle after a dilation with a scale factor of and centered at point . Is triangle congruent to triangle ? Explain your answer.
Determine and state the area of triangle , whose vertices have coordinates , and .
A support wire reaches from the top of a pole to a clamp on the ground. The pole is perpendicular to the level ground and the clamp is 10 feet from the base of the pole. The support wire makes a angle with the ground. Find the length of the support wire to the nearest foot.
In the diagram below, circle has a radius of 10 .
If , find the area of shaded sector , in terms of .
On the set of axes below, .
Describe a sequence of rigid motions that maps onto .
In right triangle , altitude is drawn to hypotenuse , and .
Determine and state, to the nearest tenth, the length of .
Given circle with radius , use a compass and straightedge to construct an equilateral triangle inscribed in circle . [Leave all construction marks.]
In the diagram below of circle and are chords, and . If , the area of the shaded sector is
In circle below, diameter , radius , and chord are drawn. If and , then the area of sector is
A circle with a diameter of 10 cm and a central angle of is drawn below. What is the area, to the nearest tenth of a square centimeter, of the sector formed by the angle?
The diagram below models the projection of light from a lighthouse, . The sector has a radius of 38 miles and spans .
Determine and state the area of the sector, to the nearest square mile.
\begin{aligned} & \frac{102}{360} \times \pi r^{2}=A \text { of sector } \\ & \frac{102}{360} \times \pi 38^{2}=A \text { of sector } \\ & \frac{102}{360} \times \pi 14444=A \text { of sector } \\ & \frac{102}{360} \times 4536.4598=A \text { of sector } \\ & 1285.3303=A \text { of sector } \\ & 1285 \mathrm{mi}^{2}=A \text { of sector } \end{aligned}$$The student gave a complete and correct response.
In the diagram below of circle , the area of the shaded sector is and the length of is 6 inches. Determine and state .
Determine and state .
The area of a sector of a circle with a radius measuring 15 cm is . What is the measure of the central angle that forms the sector?