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Tangents Section 10.5

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Definition: Tangent A tangent is a line in the plane of a circle that intersects the circle in exactly one point.

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Tangent Radius Theorem If a radius is drawn to the point of contact then the tangent is perpendicular to the radius. If is tangent to circle P, then

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Two Tangent Theorem If two tangent segments are drawn to a circle from an external point, then those segments are congruent. If are tangent and share point S as an endpoint, then

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Example 1 Find x. Assume that all segments that appear to be tangent are tangent. CD = 8, CE = 5 Decide which angle must be the right angle and set up Pythagorean Theorem must be the right angle so

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Ex. 2 Find x. Assume that segments that appear to be tangent are tangent.

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Ex 3 Assume that all segments that appear to be tangent are tangent. Find ST.

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Ex 4 Is tangent to the circle? Why or why not?

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Ex 5 Find the perimeter of the polygon given that all sides that appear to be tangent are tangent.

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Homework: Pg. 593 5 – 22, 37, 39 - 42

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