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. [br][br][b]Be sure to move points C &/or A around after completing each step below.[/b] There is also a point to change the circle's radius (if you wish). [br][br]Instructions: [br][br]1) Construct radius AE & radius AD. [br]2) Find the measure of angle CEA & angle ADC.[br]3) Move point [color=#1551b5]C[/color] around. What do you notice about the two angle measures you obtained in step (2)? Use what you have noticed to answer the question below.
[i]Let's generalize now. [/i] Fill in the blanks: [b]If a line is drawn tangent to a circle, then that line is always _________________________ to the radius of that circle drawn to the point of tangency. [/b]
4) Click on the red "[color=#c51414]Show Segments Tangent to Circle[/color]" icon. [br]5) Measure the lengths [color=#c51414]CE[/color] & [color=#c51414]CD[/color]. What do you notice? [br]6) Move point [color=#1551b5]C[/color] around. What do you notice about the lengths of the 2 [color=#c51414]tangent segments[/color] you obtained in (5) above?
[i]Let's generalize again:[/i] [b][color=#c51414]Tangent segments[/color] drawn to a circle from a [color=#1551b5]point outside the circle[/color] are _____________ .[/b]