Key Theorems on Circle Tangents
Theorem 1 (Perpendicularity of Tangent and Radius):
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
$$OP \perp XY \quad (\text{where } P \text{ is point of contact})$$
Theorem 2 (Tangents from an External Point):
The lengths of tangents drawn from an external point to a circle are equal.
$$PA = PB$$
