Congruent Triangles std8 Page-28.5 EM

Circle Geometry | Chords AB, AC, BC | Are AB and AC equal?

⚪ Circle with center O 📍 A (apex/top), B (bottom left), C (bottom right) 📐 ∠AOB = ∠AOC = 60° 🔴 AB, AC, BC are chords (red lines)

✍️ Analyze Chords AB and AC

1 Identify the central angles

What are the given central angles in the figure?

2 Central angle subtended by chord AB

Which central angle does chord AB subtend at the center?

3 Central angle subtended by chord AC

Which central angle does chord AC subtend at the center?

4 Compare the central angles

What is the relationship between ∠AOB and ∠AOC?

5 Chord length theorem

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

6 Triangle congruence

Consider triangles AOB and AOC. Which sides are equal?

7 Congruence of triangles

Are triangles AOB and AOC congruent? If yes, by which criterion?

8 Corresponding sides from congruence

From the congruence, what can we say about AB and AC?

9 Final answer

Are the lines AB and AC equal?

10 Reason for equality

Why are AB and AC equal?

⚪ Circle Geometry | Chords AB, AC, BC