High School Geometry Practice - Circles

Common Core Practice


This quiz is designed in accordance with the following Common Core State (CCS) standards:

QuestionCommon Core Standard #
indicates a modeling standard.
+ indicates a college and career ready standard.

All questions of this quiz illustrate the difficulty of the high school G.C standards required for all students, including the college and career ready students.

Questions 1 and 2: Triangle ABC in the figure below is inscribed in circle C of center O. Suppose D is the midpoint of segment AC and E is the midpoint of segment BC. What is the circumference of the circle if the segment OD measures 2 cm?

The quadrilateral with vertices D, O, E and C in the figure above is a:

Question 3: Triangles ABD and BAC are inscribed in the same semicircle of a circle with center O, as shown in the figure below. Triangles ABD and BAC are congruent if:

Question 4: The center O of the circle inscribed in any triangle is the point of intersection of the:

Question 5: A circle of radius r and center O is inscribed in a right isosceles triangle ABC. Calculate the ratio between the area of the triangle and the area of the circle:

Question 6: The 3-point line distance from the basket of a NBA basketball court is r = OC = 23.75 ft. and d = OE = 22 ft. in the corner. The distance h between the baseline AB and the basket represented by point O is h = 5 ft.
Select the best approximation of the area between the 3-point line and the baseline of this basketball half court.

Questions 7 and 8: Two congruent circles with the centers in A and C intersect each other in points B and D. Calculate the area of the quadrilateral ABCD if the radius of the circles is r = 4 cm and the distance between the centers of the circles is AC = 1.8×r.

ABCD in the figure above is a:

Question 9: Three identical cylinders are held next to each other with a rubber band. What is the approximate length of the rubber band in its extended position over the three cylinders? The radius of the bases of the cylinders is r = 5 cm.

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