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Math worksheet generator

Build a printable AMC-style set by topic and difficulty. Every worksheet includes multiple-choice questions and a worked answer key.

Mathbound · Contest practice

Similar Triangles worksheet

Mixed difficulty

Name

Date

1.
Right triangle with legs $9$ and $40$ . Hypotenuse?
- A.41
- B.40
- C.42
- D.49
- E.z4
2.
Circle radius $17$ . Chord length $30$ . Distance from center to chord?
- A.8
- B.2
- C.9
- D.17
- E.15
3.
Right triangle with legs $21$ and $72$ . Hypotenuse?
- A.76
- B.72
- C.93
- D.75
- E.74
4.
Regular $20$ -gon vertices labeled. How many triangles formed by three vertices contain the center?
- A.260
- B.240
- C.235
- D.1140
- E.400
5.
A circle has radius $15$ . A chord of length $24$ is at what distance from the center?
- A.15
- B.10
- C.3
- D.12
- E.9
6.
Circle radius $5$ . Chord length $6$ . Distance from center to chord?
- A.5
- B.3
- C.4
- D.2
- E.z4
7.
Regular $16$ -gon vertices labeled. How many triangles formed by three vertices contain the center?
- A.112
- B.107
- C.560
- D.256
- E.128
8.
Right triangle with legs $9$ and $12$ . Hypotenuse?
- A.3
- B.16
- C.14
- D.21
- E.15
9.
Regular $15$ -gon vertices labeled. How many triangles formed by three vertices contain the center?
- A.455
- B.225
- C.155
- D.140
- E.135
10.
Circle radius $15$ . Chord length $18$ . Distance from center to chord?
- A.9
- B.12
- C.6
- D.13
- E.15

Answer key · worked solutions

1. A. 41
Pythagorean theorem / scaled triples. $\sqrt{(9)^2+(40)^2}$ . $41$ .
2. A. 8
Right triangle: half-chord, radius, distance. $\sqrt{17^2-15^2}$ . $8$ .
3. D. 75
Pythagorean theorem / scaled triples. $\sqrt{(21)^2+(72)^2}$ . $75$ .
4. B. 240
Each arc between vertices $<n/2$ . Count valid triples. $240$ .
5. E. 9
Right triangle: half-chord, radius, distance. $\sqrt{15^2-12^2}$ . $9$ .
6. C. 4
Right triangle: half-chord, radius, distance. $\sqrt{5^2-3^2}$ . $4$ .
7. A. 112
Each arc between vertices $<n/2$ . Count valid triples. $112$ .
8. E. 15
Pythagorean theorem. $\sqrt{9^2+12^2}$ . $15$ .
9. D. 140
Each arc between vertices $<n/2$ . Count valid triples. $140$ .
10. B. 12
Right triangle: half-chord, radius, distance. $\sqrt{15^2-9^2}$ . $12$ .

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Free AMC Math Worksheet Generator — Mathbound