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Tangents and Secants. Advanced Geometry Lesson 3 Circles. 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.
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Tangents and Secants Advanced Geometry Lesson 3 Circles
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.
Example: Triangle JKL is circumscribed about R. Find x and the perimeter of JKL. 10
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 = 76. = 88 and
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.
