Radii, Chords, Secants and Tangents

Every circle problem starts with naming what you're looking at, and the names depend on how a line relates to the circle, not on anything fancy. A radius runs from the center to the edge. A diameter is a radius doubled, stretching all the way across through the center. A chord is any segment with both endpoints on the circle, whether or not it passes through the center. A secant is a whole line that cuts through the circle, crossing it at two points, the chord is just the piece of that secant trapped inside. A tangent touches the circle at exactly one point and never crosses inside at all.

Picture one circle with all of these drawn at once: a radius sticking out from the center, a diameter lying flat across the middle, a chord off to one side not touching the center, a secant line extending past the circle in both directions, and a tangent brushing the edge. The diameter is the longest chord you can draw, since any chord not through the center is shorter. This single picture is usually enough to answer questions about which term applies to which mark on a diagram.

These definitions set up everything else in circle geometry. Central angles and inscribed angles are measured using radii and chords. Arc length and sector area problems depend on knowing the radius. And tangent lines show up again when a tangent meets a radius at a right angle, a fact used to find missing lengths in circle-and-triangle combinations. Get the vocabulary solid first, since most circle problems are really just testing whether you can read the diagram correctly.