Angles Formed by Tangents, Chords, and Secants
The measure of an angle formed by a tangent and a chord that intersect at the point of tangency is equal to one – half the measure of the intercepted arc.
The measure of an angle formed by two chords intersecting within a circle is equal to one – half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
Angles Formed by Tangents and Secants
We will study in this section three cases:
- Angles formed by two tangents
- Angles formed by a tangent and a secant
- Angles formed by two secants
The measure of an angle formed by a tangent and a secant, two secants, two secants, or two tangents intersecting outside the circle is equal to one half the difference of the measures of the intercepted arcs.
Read the explanation below to learn more about angles formed by secants, tangents, and chords.
Angles Formed by Tangents, Chords, and Secants
Practice: Find measures of arcs and angles formed by secants and tangents in the following exercises.
Angles Formed by Tangents, Chords, and Secants 1
Angles Formed by Tangents, Chords, and Secants 2