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Circle Vocabulary - Worksheet 8 - 10th Grade

Hard

Identify and describe parts of a circle (Hard)

30 problems · 10-15 minutes · Skills: circles, vocabulary, geometry

About This Worksheet

This hard-level worksheet contains 30 problems designed for 10th Grade students practicing circle vocabulary & properties. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Every subsequent circle theorem depends on precise knowledge of circle vocabulary. Students who cannot distinguish a chord from a secant, or a central angle from an inscribed angle, will struggle to apply theorems correctly. A solid vocabulary foundation makes all of circle geometry accessible.

  • Identify and label radius, diameter, chord, secant, tangent, arc, and sector
  • Distinguish between minor and major arcs and identify central angles
  • Apply the relationship between diameter and radius to calculate missing lengths
  • Identify semicircles and use them to classify inscribed angles
  • Describe the relationship between a chord and its corresponding arc

How to Solve: Worked Example

Example Problem: A chord of a circle of radius 5 lies 4 from the centre. Find the chord length.
Solution Steps:
  1. Drop a perpendicular from the centre to the chord — it bisects the chord.
  2. This forms a right triangle with hypotenuse 5 (radius) and one leg 4 (distance).
  3. The other leg is √(25 - 16) = 3, which is half the chord.
  4. The full chord is 2 × 3 = 6.
Answer: 6
Tip: The perpendicular from the centre always bisects the chord — remember to double at the end.
1
A circle has diameter 16. A radius and a tangent meet at the point of tangency — find that angle, and the radius.
2
A circle has radius 4. Find the length of its longest chord.
3
A chord of a circle of radius 41 lies 40 from the centre. Find the chord's length.
4
A chord of a circle of radius 73 lies 55 from the centre. Find the chord's length.
5
A chord of a circle of radius 20 lies 16 from the centre. Find the chord's length.
6
A circle has radius 13. Find the length of its longest chord.
7
A circle has diameter 20. A radius and a tangent meet at the point of tangency — find that angle, and the radius.
8
A circle has diameter 39. A radius and a tangent meet at the point of tangency — find that angle, and the radius.
9
A circle has radius 14. Find the length of its longest chord.
10
A chord of a circle of radius 41 lies 40 from the centre. Find the chord's length.
11
A circle has diameter 59. A radius and a tangent meet at the point of tangency — find that angle, and the radius.
12
A circle has radius 27. Find the length of its longest chord.
13
A circle has diameter 45. A radius and a tangent meet at the point of tangency — find that angle, and the radius.
14
A chord of a circle of radius 17 lies 15 from the centre. Find the chord's length.
15
A circle has radius 11. Find the length of its longest chord.
16
A circle has radius 4. Find the length of its longest chord.
17
A circle has diameter 10. A radius and a tangent meet at the point of tangency — find that angle, and the radius.
18
A chord of a circle of radius 73 lies 55 from the centre. Find the chord's length.
19
A circle has diameter 31. A radius and a tangent meet at the point of tangency — find that angle, and the radius.
20
A circle has diameter 54. A radius and a tangent meet at the point of tangency — find that angle, and the radius.
21
A circle has radius 19. Find the length of its longest chord.
22
A circle has diameter 20. A radius and a tangent meet at the point of tangency — find that angle, and the radius.
23
A circle has radius 29. Find the length of its longest chord.
24
A chord of a circle of radius 25 lies 20 from the centre. Find the chord's length.
25
A chord of a circle of radius 15 lies 12 from the centre. Find the chord's length.
26
A circle has diameter 9. A radius and a tangent meet at the point of tangency — find that angle, and the radius.
27
A chord of a circle of radius 65 lies 56 from the centre. Find the chord's length.
28
A circle has radius 17. Find the length of its longest chord.
29
A circle has radius 9. Find the length of its longest chord.
30
A circle has diameter 12. A radius and a tangent meet at the point of tangency — find that angle, and the radius.

Answer Key

1. 90°, radius 82. 83. 184. 965. 246. 267. 90°, radius 108. 90°, radius 39/29. 2810. 1811. 90°, radius 59/212. 5413. 90°, radius 45/214. 1615. 2216. 817. 90°, radius 518. 9619. 90°, radius 31/220. 90°, radius 2721. 3822. 90°, radius 1023. 5824. 3025. 1826. 90°, radius 9/227. 6628. 3429. 1830. 90°, radius 6

Frequently Asked Questions

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How do I find worksheets at different difficulty levels?

Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.

What skills does this circles worksheet cover?

This worksheet focuses on circles, vocabulary, geometry. It is designed for 10th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 30 problems. It typically takes 10-15 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.