Amiya Kumar 
🔵 Circle Geometry – Extended Concepts & Practice
This section deepens your understanding of central and peripheral angles in a circle, especially for solving advanced questions with symmetry and chords.
🔸 Concept 9: Angle at Center and Subtended Angle
If the central angle \( \angle AOB = 2\theta \), then the angle at the circumference \( \angle ACB = \theta \).
Also, \( \angle ADB = 180^\circ - \theta \) lies in the opposite arc.
🔸 Concept 10: Complete Angle Diagram from Chord
A chord creates angles on both sides of a circle. For angle \( \theta \) at the top, the angle at the base becomes \( 180^\circ - \theta \).
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