The Circle

x²+y²=r². The right-hand number is r² — square-root it for the radius.

Given a point: r² = distance². Line meets circle: sub in and solve (chord/tangent/miss). Axes: y=0 or x=0.

A tangent is perpendicular to the radius. m_r = b/a, so m_t = -a/b; then y - y₁ = m(x - x₁).

Sub a point into x²+y² and compare with r² (inside/on/outside). For a missing coordinate, solve and write ±.

(x-h)²+(y-k)²=r². Watch the signs; read the centre straight off the brackets.

Centre = midpoint of the endpoints; radius = half the diameter. Reverse the midpoint to find a missing endpoint.

Radius unchanged, only the centre moves. Central symmetry: (p,q) is the midpoint. Translation: apply the shift to the centre.