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Geometry Topics Overview Chapter Exam

Exam Instructions:

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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Question 1 1. In the image shown, the solid black curves are a trail through a wooded area, and the dotted blue line has a length of 1 mile. Based on this, what is the distance of one full loop of the trail (Start and finish at the same point shown)?

Question 2 2. In the arbelos shown, AB + BC = D (D is the diameter of the largest circle). Based on this, what is the formula for the perimeter of the arbelos?

Question 3 3. Which of the following statements is NOT true?

Question 4 4. If a bicentric quadrilateral has side lengths a, b, c, and d, what formula can we use to find its inradius?

Question 5 5. A bicycle's back wheel has a diameter of 65 cm. The back wheel axle has a diameter of 1 cm. What is the mechanical advantage of the back wheel?

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Question 6 6. Which of the following methods will give you the mechanical advantage of a wheel and axle?

Question 7 7. In the image, MO and NP are the bimedians of quadrilateral ABCD, and E is the centroid of the vertices of the quadrilateral. If MO has length 24 inches, what is the length of EO?

Question 8 8. Which of the following is a property of bimedians of a quadrilateral?

Question 9 9. If the smallest and medium circles of an arbelos have diameters 7 feet and 18 feet, respectively, what is the diameter of the largest circle of the arbelos?

Question 10 10.

Suppose an arbelos has the following properties:

  • 1/2 the perimeter of the smallest circle is 8π feet.
  • 1/2 the perimeter of the medium circle is 10π feet.
  • 1/2 the perimeter of the largest circle is 18π feet.

What is the perimeter of the arbelos?

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Question 11 11. If a regular polygon has n sides, each of length s, what is the formula we use to find the length of the polygon's circumradius?

Question 12 12. If a triangle has side lengths a, b, and c, what is the formula for the length of the triangle's circumradius?

Question 13 13. The circumcircle of a triangle describes a circle that _____.

Question 14 14. Which of these might be an appropriate use when finding the circumcenter of a triangle?

Question 15 15. Which of the following does NOT describe the circumradius of a triangle?

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Question 16 16. What is the circumradius of a triangle?

Question 17 17. Which of the following statements is NOT true?

Question 18 18. What is the Brocard Circle of a triangle?

Question 19 19. A vertex is a point where two _____ meet?

Question 20 20. Which of the following continues forever in only one direction?

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Question 21 21. Which of the following is NOT a true statement?

Question 22 22. Suppose that the circumradius of a triangle is 2.5 centimeters. What is the perimeter of the circumcircle of the triangle (rounded to one decimal place)?

Question 23 23. Which of the following is a 3-dimensional solid?

Question 24 24. What is the area of a rectangle with a width of 10cm and a length of 6cm?

Question 25 25. What mathematical equation did Archimedes create?

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Question 26 26. What is the Archimedes Principle?

Question 27 27. Which of the following gives two correct names for the plane below?

Question 28 28. Name all of the points that are in the plane below.

Question 29 29. Which of the following is not a three-dimensional object?

Question 30 30. What is the area of a triangle with a base of 12 inches and a height of 14 inches? Use 3.14 for pi.

Geometry Topics Overview Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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