Use a compass and a straightedge to construct tangent to circle at point .

1. Draw a ray from center through point and extending beyond point .
2. Put the sharp point of the compass on point . Set it to any setting less than the length of , and then draw an arc on either side of , creating points and .
3. Put the sharp point of the compass on point and set it to a width greater than the distance of . Make a large arc intersecting .
4. Without changing the compass setting, put the sharp point of the compass on point and draw a second arc that intersects the first. Label the point of intersection with the arc drawn in step 3 as point .
5. Draw a line connecting points and , creating tangent .

Use a compass and a straightedge to construct the lines tangent to circle at point .

1. Draw a ray connecting center and the given point .
2. Find the midpoint of by constructing the perpendicular bisector.
3. Put the sharp point of the compass on midpoint and open the compass to point . 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 and .
4. Use a straightedge to draw a line from point to point and a second line from point to point .