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 G. Find the perimeter of HJK if NK = JL + 29.

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

Secant

whether they are both secants, 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 On 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. Find x.