Congruent Triangles std8 Page-28.4 EM

Circle Geometry | Chords AB and CD | Are they equal?

⚪ Circle with center O 📍 Points: A, C, D, B (clockwise) 📐 ∠AOB = 80°, ∠BOC = 80° 🔴 AB and CD are chords (red lines)

✍️ Analyze the Chords AB and CD

1 Central angles

What are the given central angles?

2 Identify ∠COD

Points on the circle are A, C, D, B in clockwise order. What is ∠COD?

3 Central angle subtended by chord AB

Chord AB subtends which central angle?

4 Central angle subtended by chord CD

Chord CD subtends which central angle?

5 Chord length theorem

In a circle, if two chords subtend equal central angles, what can we say about their lengths?

6 Compare ∠AOB and ∠COD

What is the relationship between ∠AOB and ∠COD?

7 Conclusion about chord lengths

Since ∠AOB = ∠COD, what can we say about AB and CD?

8 Geometric reasoning

Why does equal central angles imply equal chords?

9 Final answer to the question

Are the lines AB and CD equal?

10 Final reasoning

Why are AB and CD equal?

⚪ Circle Geometry | Chords AB and CD