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9.2 Tangents and Secants

9.2 Tangents and Secants. Tangents and secants are LINES. A tangent line intersects the circle at exactly ONE point. A secant line intersects the circle at exactly TWO points. A little extra information. The word tangent comes from the Latin word meaning to touch

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9.2 Tangents and Secants

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  1. 9.2 Tangents and Secants Tangents and secants are LINES. A tangent line intersects the circle at exactly ONE point. A secant line intersects the circle at exactly TWO points.

  2. A little extra information • The word tangent comes from the Latin word meaning to touch • The word secant comes from the Latin word meaning to cut.

  3. Important Theorems • Tangent Theorem: • If a line is tangent to a circle, then the line is perpendicular to a radius of the circle drawn to the point of tangency. The line AB is tangent to circle C at B. How could we prove that segment CB and line AB are perpendicular?

  4. Converse of the Tangent Theorem • Go waaaayyy back… how do we get a converse statement? • What would be the Converse of the Tangent Theorem? • If a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.

  5. Radius and Chord Theorem • A radius that is perpendicular to the chord of a circle bisects the chord. QR = 3 What is the measure of RS? XR = 7 and WR = 2 Find the missing measures of the remaining segments. RZ = RY = XW = WZ = XZ = 7 7 6.7 6.7 13.4

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