30. Tangents to Circles

Tangents to Circles Std – MM2G3 – Understand properties of circles EQ – What are the rules for tangents?

Vocabulary A tangent is a line that intersects a circle at exactly one point. The point at which a tangent intersects a circle is called the point of tangency.

Tangents between circles Common internal tangent – a tangent of 2 circles that intersects the line connecting the centers Common external tangent – a tangent of 2 circles that does not intersect the line connecting the centers

Name the segments

Fact #1 A line is tangent to a circle if and only if it is perpendicular to the radius drawn to the point of tangency. radius 90 degrees = perpendicular tangent

Example Since a radius of the circle is 5, any radius is 5… Since it is a radius drawn to a point of tangency, it is perpendicular to the tangent. 5 a2 + b2 = c2 122 + 52 = c2 144 + 25 = c2 169 = c2 13 = c ? This whole length is 13. x + 5 = 13 x = 8 5 12 ANSWER: x = 8

Example Find KY

Fact #2 If two segments from the same exterior point are tangent to a circle, then they are congruent. tangent #1 exterior point tangent #2 They are congruent.

Example exterior point Because of Fact #2, x=14.

Example Find x

Assignment Pg. 186: #12-20 even

Assessment Cube with partner