Integrated Math 2 / Unit 8: Circles
8.3 Tangents
Notes
A tangent touches a circle at exactly one point.
- A tangent is perpendicular to the radius at the point of tangency.
- Two tangents from the same outside point are congruent.
- Example: radius 5 and the outside point is 13 from the center: tangent length $\displaystyle = \sqrt{13^2 - 5^2} = 12$.
- Use the right triangle formed by the radius, the tangent and the segment to the center.
Practice
A point is 13 units from the center of a circle with radius 5. How long is the tangent segment from the point to the circle?
The tangent is perpendicular to the radius: $\displaystyle \sqrt{13^2 - 5^2} = \sqrt{144} = 12$.
Two tangent segments are drawn to a circle from the same outside point. One has length 9. What is the length of the other?
Tangent segments from the same point are congruent.
Point $A$ is on a circle with center $O$. Line $AP$ is tangent at $A$, and $\angle AOP = 60°$. What is $\angle APO$?
$\angle OAP = 90°$, so $\angle APO = 180° - 90° - 60° = 30°$.
Ready for more? Take the Unit 8 test.