Geometry & measures · Circles, arcs & sectors
Chapter 1 · 3
The idea
Tangents, chords & the alternate segment
Why a tangent meets a radius at 90°, why two tangents from a point are equal, why the perpendicular from the centre bisects a chord, and the alternate segment theorem.
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In this lesson — start anywhere
Geometry & measures · Circles, arcs & sectors
Tangents, chords & the alternate segment
Why a tangent meets a radius at 90°, why two tangents from a point are equal, why the perpendicular from the centre bisects a chord, and the alternate segment theorem.
Why it works
Tangent meets radius at 90°
A tangent is perpendicular to the radius at the point of contact. A tangent touches the circle exactly once, so every other point on it lies outside the circle — further from the centre. The point of contact is therefore the closest point of the tangent to the centre, and the shortest distance from a point to a line is always the perpendicular. So the radius meets the tangent at — the right angle that starts nearly every tangent calculation.Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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