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Lesson

Tangents

A tangent is a straight line that touches the circle at exactly one point. This point is known as the point of contact. A fundamental property of tangents is that the tangent to a circle is always perpendicular to the radius at the point of contact. This creates right angles, which are frequently used in proving other properties within circle geometry.

45min lesson

Objectives3 goals Lesson12 blocks Review11 assets Practice32 items

Learning objectives

What to understand

3 goals

Start lesson

Understand tangents in the Circles chapter.
Connect the idea with formulas, examples, and exam-style questions.
Use flashcards, notes, MCQs, and LAQs to check readiness.

Lesson

Step-by-step lesson

12 sections

Concept

Angle Subtended at the Center

The angle formed at the center of a circle by an arc is twice the angle formed by the same arc at the circumference. 💡 Exam Tip: Quote the correct theorem before using it. In angle problems, identify whether the angle is at the center, circumference, or formed by a tangent. ⚠️ Common Mistake: Students often apply the wrong circle theorem because they do not identify the exact figure correctly. 📌 Trigger: Name the theorem first

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Study path

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12 lesson sections7 cards / 4 notes18 MCQs / 14 written questions

Lesson Notes Flashcards Revision MCQs Written answers Topic test

Notes

Note highlights

4 notes

Review the compact notes before moving into recall.

Open notes

1
Tangent to a Circle and Point of Contact
2
Length of Tangents Drawn from an External Point
3
Alternate Segment Theorem
4
Constructions Involving Circles

Practice

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32 prompts

18 MCQs14 LAQsMixed test

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In this chapter

Circles

Topic 5 of 7

Now on Tangents. Next up: Alternate Segment Theorem.

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Circles
Chords and Cyclic Quadrilaterals
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Circles
Alternate Segment Theorem
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Tangents

What to understand

Step-by-step lesson

Angle Subtended at the Center

Angle Subtended at the Center example

Angles in the Same Segment

Angles in the Same Segment example

Angle in a Semicircle

Angle in a Semicircle example

Cyclic Quadrilaterals

Cyclic Quadrilaterals example

Finding an Angle Subtended by a Diameter

Tangent to a Circle and Point of Contact

Length of Tangents Drawn from an External Point

Alternate Segment Theorem

Angle Subtended at the Center

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Note highlights

Tangent to a Circle and Point of Contact

Length of Tangents Drawn from an External Point

Alternate Segment Theorem

Constructions Involving Circles

Check this topic

Circles

Mark this topic complete

Around this topic

Tangents

What to understand

Step-by-step lesson

Angle Subtended at the Center

Angle Subtended at the Center example

Angles in the Same Segment

Angles in the Same Segment example

Angle in a Semicircle

Angle in a Semicircle example

Cyclic Quadrilaterals

Cyclic Quadrilaterals example

Finding an Angle Subtended by a Diameter

Tangent to a Circle and Point of Contact

Length of Tangents Drawn from an External Point

Alternate Segment Theorem

Angle Subtended at the Center

Choose your next activity

Note highlights

Tangent to a Circle and Point of Contact

Length of Tangents Drawn from an External Point

Alternate Segment Theorem

Constructions Involving Circles

Check this topic

Circles

Mark this topic complete

Around this topic