Properties of Circles

A circle is defined by a fixed centre and a constant radius, but its true character emerges when you examine the relationships between its points, chords, and tangents. These properties — like the perpendicular from the centre bisecting a chord, or the equal lengths of tangents from an external point — are not just theorems; they are the geometric logic that makes coordinate calculations elegant. Understanding why these hold gives you a powerful shortcut: instead of solving long equations, you can often deduce the answer from symmetry and distanc …