In the applet below, note the circle with [color=#ff7700]center [/color][i][color=#ff7700]A[/color]. [br][/i]You can alter the radius by dragging the [color=#ff7700]orange point[/color] on the circle. [br][br][color=#0000ff]Point [i]B[/i] is a point on the circle. [/color][br][color=#0000ff]Point [i]C[/i] is a point that lies outside the circle.[/color] [br]Feel free to alter the locations of any of these 4 points at any time. [br][br]1) Use the TANGENTS [icon]/images/ggb/toolbar/mode_tangent.png[/icon] tool to construct a line through [i]B[/i] that is tangent to the circle. [br]2) Use the TANGENTS tool to construct a line passing through [i]C[/i] that is tangent to the circle. [br] What do you notice? [br][br]3) Use the INTERSECT [icon]/images/ggb/toolbar/mode_intersect.png[/icon] tool to plot the point(s) at which these tangents intersect the circle.[br] GeoGebra should name these points [i]D[/i] and [i]E[/i]. [br][br]Further directions appear below the applet.
4) Construct 2 radii with endpoint [i]A[/i] (obviously) and other endpoint located at each of the points you [br] constructed in step (3).
Measure the angle at which each radius meets each tangent. What do you notice?
It's a right angle! [br][b][br]Teachers:[/b][br]Here is one easy means for students to discover that if a radius of a circle is drawn to a tangent line (at its point of tangency), then that radius is perpendicular to that tangent.
Use the DISTANCE OR LENGTH [icon]https://www.geogebra.org/images/ggb/toolbar/mode_distance.png[/icon] tool to measure the distance from [i]C[/i] to [i]D[/i] and the distance from [i]C[/i] to [i]E[/i]. What do you notice? [br]
[math]CD=CE[/math][br][b][br]Teachers:[/b][br]Here is a means for students to discover that tangent segments drawn to a circle (from a point outside that circle) are congruent.
[color=#0000ff]When you're done (or if you're unsure of something) feel free to check by watching the brief silent screencast below the applet. [/color]