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....