Angle between a tangent and a chord

There is a direct relationship between a tangent and a chord that leave the same point too: the angle they form is equal to the inscribed angle that subtends the same arc.

Theorem — Angle between a tangent and a chord

The angle formed by a tangent to a circle and a chord leaving the point of tangency is equal to half the arc subtended by the chord (that is, it is congruent to the inscribed angle that subtends the same arc): $\widehat{\text{tangente--corda}} = \frac{\text{arco}}{2}.$

The angle $\alpha$ between the tangent at $A$ and the chord $AB$ is half the subtended arc $AB$.

Links

Topics: Euclidean circle
Concepts: Inscribed angle · Chord · Tangent
Skills: Synthetic geometry