Geo EOC Review: Circles and Coordinate Geometry

Quadrilateral 𝐴𝐵𝐶𝐷 is inscribed in circle 𝑂.

What is the measure of ∠𝐵?

• 24°

• 68°

• 90°

• 112°

The shaded area of circle 𝑂 below represents a 226° sector with area of 17.75 square units. What is the radius of circle 𝑂? Round your answer to the nearest whole unit.

HINT: USE AREA OF A SECTOR FORMULA

• 2

• 3

• 4

• 9

A farm uses an irrigation system to water crops in a circular pattern, as shown in the diagram below. The rotating arm is 50 meters in length.

As the arm rotates through an angle of 100°, it forms a circular arc. What is the length, in meters, of the arc?

• 43.6

• 87.3

• 157.1

• 314.2

The points (−5, 0) and (1, 8) are the endpoints of a diameter of a circle. What is the standard equation of the circle?

On a coordinate plane, circle 𝑂 has its center at the point (3, −6). The point 𝑃(−1, −2) is on circle 𝑂. Which of these statements are correct? Choose All that are correct.

• The radius of the circle is 4√2.

• C. The range of the circle is (−6 − 4√2) ≤ 𝑦 ≤ (−6 + 4√2)

• The point (4, −0.5) is on the circle

• The area of the circle is 32𝜋 square units.

On the number line below point P has a weight of 80% and point Q has a weight of 20%. What is the weighted average of points P and Q?

• −2.8

• −1.6

• 1.6

• 7.2

Point 𝑅 divides a line segment with endpoints 𝑃(−2, 6) and 𝑄(4, 15) in the ratio such as that 𝑃𝑅: 𝑅𝑄 = 1: 2.

What are the coordinates of point 𝑅?

• (0, 9)

• (2, 12)

• (9, 0)

• (12, 2)

Triangle 𝐴𝐵𝐶 is shown below. Select All the true statements.

• 𝐴𝐵𝐶 is an acute triangle.

• 𝐴𝐵𝐶 is a right triangle.

• 𝐴𝐵𝐶 is an obtuse triangle.

• 𝐴𝐵𝐶 is a scalene triangle.

• 𝐴𝐵𝐶 is an isosceles triangle.

The ordered pairs that describe the locations of three vertices of a parallelogram on a coordinate plane are given. (−2, −1) (−2, 5) (2, 4).

Which ordered pair describes a possible location of the fourth vertex of the parallelogram?

HINT: USE GRAPH PAPER.

• (2, −2)

• (−2, 2)

• (0, 2)

• (2, 0)

A landscape artist is designing a stone walkway that crosses a flower garden. In the diagram of the walkway below, each unit represents 1 foot.

What is the area, in square feet, of the stone walkway?

• 4

• 9

• 13

• 22