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Tangents

Tangents. A line is tangent to a circle if it intersects the circle in exactly one point. This point is called the point of tangency. Consider the following diagram:. Theorem 10.9:. 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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Tangents

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  1. Tangents

  2. A line is tangent to a circle if it intersects the circle in exactly one point. This point is called the point of tangency.

  3. Consider the following diagram:

  4. Theorem 10.9: • If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

  5. Example: If RT is tangent to Circle O, Then ORRT

  6. Example:

  7. Theorem 10.10: The converse of the last theorem is also true. This means: In a plane, if a line is perpendicular to a radius of a circle at the endpoint on the circle, then the line is a tangent of the circle. If ORRT, RT is tangent to Circle O

  8. Example:

  9. Theorem 10.11: • If two segments from the same exterior point are tangent to a circle, then the two segments are congruent. Example: ABCB

  10. Example x+4 y 10 y-5

  11. Circumscribed polygons: A polygon is circumscribed about a circle if each side of the polygon is tangent to the circle. • Example:

  12. Example: Triangle HJK is circumscribed about circle G. Find the Perimeter of HJK if NK = JL+29. 45 JL + 29 18

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