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Tangent Lines - Worksheet 3 - 10th Grade

Easy

Apply properties of tangent lines to circles (Easy)

15 problems · 20-25 minutes · Skills: circles, tangents, geometry

About This Worksheet

This easy-level worksheet contains 15 problems designed for 10th Grade students practicing tangent lines. Easy worksheets use simpler numbers and straightforward problem types to build confidence and reinforce foundational skills.

Tangent line properties have direct applications in physics (tangential velocity, circular motion) and engineering (gear systems, pulleys, track design). They also introduce students to limit-based thinking — a tangent line touches a circle at exactly one point — which foreshadows calculus concepts.

  • Prove and apply the theorem that a tangent is perpendicular to the radius at the point of tangency
  • Apply the Two-Tangent Theorem to find equal tangent segment lengths
  • Solve problems involving angles and segments formed by tangents and secants
  • Calculate the length of a tangent segment from an external point using the Pythagorean Theorem
  • Apply the secant-tangent angle theorem to find intercepted arc measures

How to Solve: Worked Example

Example Problem: A tangent meets the radius at the point of tangency at what angle?
Solution Steps:
  1. A tangent touches the circle at exactly one point.
  2. The radius drawn to that point is perpendicular to the tangent.
  3. So the angle is 90°.
Answer: 90°
Tip: This right angle is what lets you use the Pythagorean theorem in almost every tangent problem.
1
Tangent segments from the same external point are…
2
How many tangents can be drawn to a circle from an external point?
3
How many points does a tangent share with a circle?
4
Tangent segments PA and PB are drawn from external point P. If PA = 35, find PB.
5
Tangent segments PA and PB are drawn from external point P. If PA = 24, find PB.
6
How many tangents can be drawn from a point on the circle?
7
Tangent segments PA and PB are drawn from external point P. If PA = 23, find PB.
8
A tangent line meets the radius drawn to the point of tangency at what angle?
9
Tangent segments PA and PB are drawn from external point P. If PA = 29, find PB.
10
Tangent segments PA and PB are drawn from external point P. If PA = 30, find PB.
11
Tangent segments PA and PB are drawn from external point P. If PA = 8, find PB.
12
How many tangents can be drawn from a point inside the circle?
13
How many tangents can be drawn to a circle from an external point?
14
A tangent line meets the radius drawn to the point of tangency at what angle?
15
How many tangents can be drawn to a circle from an external point?

Answer Key

1. congruent2. 23. 14. 355. 246. 17. 238. 90°9. 2910. 3011. 812. 013. 214. 90°15. 2

Frequently Asked Questions

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What skills does this circles worksheet cover?

This worksheet focuses on circles, tangents, 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 15 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.