9. Circles

Circles

This section explores the properties and theorems associated with circles, focusing on angles subtended by chords and the relationship between chord lengths and distances from the center.

Angle Subtended By A Chord At A Point

This section explores the angles subtended by chords at different points within a circle, emphasizing the relationship between chord lengths and the angles they subtend.

Perpendicular From The Centre To A Chord

The section discusses the properties of the perpendicular drawn from the center of a circle to a chord, including its ability to bisect the chord and its relation to the concept of distance from the center.

Equal Chords And Their Distances From The Centre

This section explores the relationship between equal chords in a circle and their distances from the center, detailing several key theorems and proofs.

Angle Subtended By An Arc Of A Circle

This section explains the relationship between chords and arcs in a circle, focusing on the angles they subtend at the center.

Cyclic Quadrilaterals

Cyclic quadrilaterals have all four vertices on a circle, leading to specific properties regarding their angles.

Summary

This section summarizes important concepts related to circles, including relationships involving chords, angles, and congruency.