36 Tangents to Circles Tangents to Circles Std

36. Tangents to Circles

Tangents to Circles Std – MM 2 G 3 – Understand properties of circles EQ – What are the rules for tangents?

Fact #1 • A tangent line is ALWAYS perpendicular to the radius of the circle drawn to the point of tangency. s iu rad 90 degrees = perpendicular tan ge nt

What this fact means…. • What this means is that you can make a right triangle and use the pythagorean theorem to find distances. s iu rad tan ge • The right angle will always be the on the outside of the circle nt

Example – Find the length of AC a 2 + b 2 = c 2 52 + 82 = c 2 25 + 64 = c 2 89 = c 2 =c

Example – find x Since a radius of the circle is 5, any radius is 5… 5 ? 12 Since it is a radius drawn to a point of tangency, it is perpendicular to the tangent. a 2 + b 2 = c 2 5 122 + 52 = c 2 144 + 25 = c 2 This whole length is 13. x + 5 = 13 x=8 169 = c 2 13 = c ANSWER: x = 8

Example • Find KY a 2 + b 2 = c 2 102 + b 2 = 242 100 + b 2 = 576 476 = b 2 =b

Example • Does this picture show a tangent? a 2 + b 2 = c 2 72 + 242 = (18+7)2 625 = 625 Yes! • It must satisfy Pythagorean Theorem

“Party Hat” Theorem • If two segments from the same exterior point are tangent to a circle, then they are congruent. tangent #1 exterior point ta ng en t# 2 They are congruent.

What this fact means…. • What this means is that you can set the 2 tangents equal to each other • Tangent 1 = tangent 2 tangent #1 ta ng en t# 2

Example exterior point x=14.

Example • Find length of tangent

Visible Horizon-Using tangents in navigation