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**Advanced Geometry Lesson 3 Circles**

Tangents and Secants

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**Tangent If a line is tangent to a circle, then it is perpendicular**

to the radius drawn to the point of tangency.

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

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

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**If two segments from the same exterior point are **

tangent to a circle, then they are congruent.

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Example: Find x and y.

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

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**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

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Secant

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**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

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**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.

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

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**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.

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Example: Find m RPS if = 114 and = 136.

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**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.

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Example: Find x. Find x.

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