Chord Theorems

Tangent-Chord Theorem

Tangent-Chord Angle

An angle formed by a tangent and a chord is called a tangent-chord angle. In the diagram, angle BAT is a tangent-chord angle.

There are 3 conditions for a tangent-chord angle.
1. One side of the angle is a tangent to the

circle.

2. Another side of the angle is a chord (or

cuts the circle).

3. The vertex of the angle lies on the circle.

Open Ended

Explain if $$\angle ABC$$ is a tangent-chord angle.

Open Ended

Explain if $$\angle ABC$$ is a tangent-chord angle.

Open Ended

Explain if $$\angle ABC$$ is a tangent-chord angle.

Open Ended

Explain if $$\angle ABC$$ is a tangent-chord angle.

Open Ended

Is this a tangent-chord angle? If no, explain why.

Open Ended

Explain if $$\angle ABC$$ is a tangent-chord angle.

​Tangent-Chord Theorem (Alternate Segment Theorem)

Prove that angle BAC = angle CBD.

​Identify two pairs of angles that satisfy tangent-chord theorem.

​Identify two pairs of angles that satisfy tangent-chord theorem.

​Identify two pairs of angles that satisfy tangent-chord theorem.

​Identify two pairs of angles that satisfy tangent-chord theorem.