Tangent-Chord Angle

Tangent-Chord Angle

Acute angle formed by a chord of a circle and a tangent to the circle at one of the endpoints of the chord.

Example

In the figure below, angle BAC is a tangent-chord angle to the circle with centre O. The point of tangency is the endpoint A of chord AB. Line segment AC is a tangent to the circle at point A.

Formula

In the example above, m$$\angle {\textrm{BAC}}=\frac{\textrm{m}\angle{\textrm{AOB}}}{2}$$