CIR011 · Circles · Classes 10–11
Tangent-chord theorem
The angle between a tangent and a chord through the point of contact equals the inscribed angle on the other side of the chord (the alternate segment).
∠ tangent-chordTangent-chord theorem
📐 Formula
∠(tangent, chord) = inscribed angle in alternate segment
✏️ Worked example
If the chord AB makes 40° with the tangent at A, every inscribed angle on the far arc is 40° (central angle 80°).
🌍 Where it is used
Circle geometry proofs and design.
❓ Quick check
Tangent-chord angle 55°. Inscribed angle in the alternate segment?
🏋️ Practice
EasyCentral angle on the same chord, if the tangent-chord angle is 30°?
Answer: 60°
MediumTangent-chord angle when the chord is a diameter?
Answer: 90°
ChallengeWhat is this theorem also called?
Answer: The alternate segment theorem