Tangents Section 10.5. 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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Presentation transcript:

Tangents Section 10.5

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

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

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

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

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

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

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

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

Homework:  Pg – 22, 37,