Advanced Geometry Lesson 3 Circles Tangents and Secants

Advanced Geometry Lesson 3 Circles Tangents and Secants

Tangent If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

Example: is tangent to A at point C. Find x.

Example: Determine whether is tangent to F. Justify your reasoning.

If two segments from the same exterior point are tangent to a circle, then they are congruent.

Example: Find x and y.

Example: Triangle HJK is circumscribed about Find the perimeter of HJK if NK = JL + 29. G.

Example: Triangle JKL is circumscribed about Find x and the perimeter of JKL. 10 R.

Secant

Two segments, whether they are both secants, both tangents, or one secant and one tangent, can intersect in one of three places: In the Circle Outside the Circle

Intersections Inside a Circle If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Example: Find m 4 if = 88 and = 76.

Intersections On a Circle 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: Find m RPS if = 114 and = 136.

Intersections Outside of a Circle If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Example: Find x.