Lesson 12 · The Relation between Opposite Angles of a Cyclic Quadrilateral

Relation between the Central Angle and Inscribed Angle Presentation

MathematicsSubject
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Class 10 Mathematics · Circle

Central Angle and Inscribed Angle

Theorem 1 · Angle in a semicircle · Theorem 2

What we will be able to do

📐

Tell a central angle from an inscribed angle

✌️

Prove the central angle is double

🔲

Show the angle in a semicircle is a right angle

🟰

Use equal inscribed angles on the same arc

Two kinds of angle

🎯Central angle
Vertex at the centre O
Arms are radii
Same size as its arc
VS
⭕Inscribed angle
Vertex on the circle
Arms are chords
Half of its arc

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Presenter notes: Today we find how two kinds of angles in a circle are related, and two results that follow from it.