Use a compass and a straightedge to construct [math]\overline{BC}[/math] tangent to circle [math]A[/math] at point [math]B[/math].

[list=1][br][*]Draw a ray from center [math]A[/math] through point [math]B[/math] and extending beyond point [math]B[/math].[br][*]Put the sharp point of the compass on point [math]B[/math]. Set it to any setting less than the length of [math]\overline{AB}[/math] , and then draw an arc on either side of [math]B[/math], creating points [math]D[/math] and [math]E[/math].[br][*]Put the sharp point of the compass on point [math]D[/math] and set it to a width greater than the distance of [math]\overline{DB}[/math]. Make a large arc intersecting [math]\overrightarrow{AB}[/math].[br][*]Without changing the compass setting, put the sharp point of the compass on point [math]E[/math] and draw a second arc that intersects the first. Label the point of intersection with the arc drawn in step 3 as point [math]C[/math].[br][*]Draw a line connecting points [math]C[/math] and [math]B[/math], creating tangent [math]\overleftrightarrow{BC}[/math].[br][/list][br][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url=http://www.walch.com]www.walch.com[/url] for more information.

Use a compass and a straightedge to construct the lines tangent to circle [math]C[/math] at point [math]D[/math].

[list=1][br][*]Draw a ray connecting center [math]C[/math] and the given point [math]D[/math].[br][*]Find the midpoint of [math]\overline{CD}[/math] by constructing the perpendicular bisector.[br][*]Put the sharp point of the compass on midpoint [math]G[/math] and open the compass to point [math]C[/math]. Without changing the compass setting, draw an arc across the circle so it intersects the circle in two places. Label the points of intersection as [math]H[/math] and [math]J[/math].[br][*]Use a straightedge to draw a line from point [math]D[/math] to point [math]H[/math] and a second line from point [math]D[/math] to point [math]J[/math].[br][/list][br][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url=http://www.walch.com]www.walch.com[/url] for more information.