Secants, Tangents and Angle Measures

Definition - Secant

Theorem – Secant-Secant Angle If 2 secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Example 1 – Secant-Secant Angle Compute the measure of angle 2 if the measurement of arc BC is 30 and for arc AD is 20.

Example 1 – Secant-Secant Angle Compute the measure of angle 2 if the measurement of arc BC is 30 and for arc AD is 20. By the previous theorem,

Example 1 – Secant-Secant Angle Compute the measure of angle 2 if the measurement of arc BC is 30 and for arc AD is 20. By the previous theorem,

Example 1 – Secant-Secant Angle Compute the measure of angle 2 if the measurement of arc BC is 30 and for arc AD is 20. By the previous theorem,

Example 1 – Secant-Secant Angle Compute the measure of angle 2 if the measurement of arc BC is 30 and for arc AD is 20. By the previous theorem,

Example 1 – Secant-Secant Angle Compute the measure of angle 2 if the measurement of arc BC is 30 and for arc AD is 20. By the previous theorem,

Example 2 – Secant-Secant Angle Compute the measurement of angle 4

Example 2 – Secant-Secant Angle Compute the measurement of angle 4 By the previous theorem

Example 2 – Secant-Secant Angle Compute the measurement of angle 4 By the previous theorem

Example 2 – Secant-Secant Angle Compute the measurement of angle 4 By the previous theorem

Example 2 – Secant-Secant Angle Compute the measurement of angle 4 By the previous theorem

Example 2 – Secant-Secant Angle Compute the measurement of angle 4 By the previous theorem

Example 2 – Secant-Secant Angle Compute the measurement of angle 4 By the previous theorem

Theory – Secant-Tangent Angle If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one-half the measure of its intercepted arc.

Example 3 – Secant-Tangent Angle Compute the measurement of angle ABC

Example 3 – Secant-Tangent Angle Compute the measurement of angle ABC

Example 3 – Secant-Tangent Angle Compute the measurement of angle ABC

Example 3 – Secant-Tangent Angle Compute the measurement of angle ABC

Example 3 – Secant-Tangent Angle Compute the measurement of angle ABC

Theorem For any variation of secants and tangents that intersect outside of the circle, the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Example 4 – Secant-Tangent Angle