Properties of Tangents
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)? Use what you have noticed to answer the question below.
Let's generalize now. Fill in the blanks: 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.
Use the applet above to perform the following actions.
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?
Based upon what you noticed in (5)/(6) above, fill in the blank below.
Let's generalize again: Tangent segments drawn to a circle from a point outside the circle are _____________ .