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GeoGebraGeoGebra Classroom

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)? 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.