# Properties of Tangents

- Author:
- Tim Brzezinski

- Topic:
- Circle, Tangent Line or Tangent

Definition: A line is said to be TANGENT to a circle if and only if it intersects the circle in exactly 1 point. In the applet below, the tangent lines are drawn in purple. Points E and D are said to be points of tangency.

**Be sure to move points C &/or A around after completing each step below.**There is also a point to change the circle's radius (if you wish). Instructions: 1) Construct radius AE & radius AD. 2) Find the measure of angle CEA & angle ADC. 3) Move point C around. What do you notice about the two angle measures you obtained in step (2)?*Let's genearalize now.*Fill in the blanks:**If a line is drawn tangent to a circle, then that line is always(_________________________) to the (__________________) of that circle drawn to the point of (_____________________).**4) Click on the red "Show Segments Tangent to Circle" icon. 5) Measure the lengths CE & CD. What do you notice? 6) Move point C around. What do you notice about the lengths of the 2 tangent segments you obtained in (5) above?*Let's generalize again:***Tangent segments drawn to a circle from a point outside the circle are....**Activity questions appear above the applet.