Drawing two lines tangent to circle from an exterior point P
Step 1. Draw the segment PC.Step 2. Draw the perpendicular bisector of the segment PC and label the midpoint M.
Step 3. Use centre point M and radius MP. Draw a circle that intersects the first circle at points A and B.
Step 4. Draw the lines PA and PB. These lines are tangent to the circle with centre C.
Construct tangent circles with radius m and r
Step 1. Draw a circle with centre A and radius r.Step 2. From A, draw a ray that intersects the circle at C.
Step 3. Use centre point C and radius m. Draw an arc that intersects the ray AC at point B. Draw another arc that intersects it at D.
Step 4. Use centre point B and radius m. Draw an exterior tangent circle. Then use centre point D and radius m. Draw an interior tangent circle to the one with radius r.
Construct exterior tangents to two circles with radius r and r'
Step 1. Draw the segment AB.Step 2. Draw the perpendicular bisector of the segment AB and find the midpoint M.
Step 3. Use centre point M and radius MA. Draw a circle.
Step 4. Use centre point A and a radius equal to the difference between r and r'. Draw a circle that intersects the circle with centre M, and obtain points C and D.
Step 5. Draw the lines AC and AD to obtain points E and F.
Step 6. Draw the lines BG and BH parallel to AE and AF, respectively.
Step 7. Draw the lines EG and FH. These lines are the exterior tangents to the two given circles.
Construct interior tangents to two circles
Step 1. Draw the segment IJ.Step 2. Draw the perpendicular bisector of the segment IJ and label the midpoint K.
Step 3. Use centre point K and radius KJ. Draw a circle, obtaining points L and M at its intersections with the perpendicular bisector of the segment IJ.
Step 4. Use centre / and a radius equal to the sum of the radii r and r'. Draw a circle that passes through points L and M.
Step 5. Draw the lines IL and /M to obtain points N and O.
Step 6. Draw a line parallel to line IL that passes through point J to obtain point Q.
Step 7. Draw a line parallel to line /M that passes through point J to obtain point P.
Step 8. Draw the lines NQ and OP. These lines are the interior tangents to the two given circles.
Linking a circle and a straight line with an arc whose radius ( r) is less than the radius of the circle
Step 1. Draw a parallel line to AB at a distance r.Step 2. Use centre point O and a radius equal to the sum of the radius m and r. Draw an arc that intersects the parallel line at point C.
Step 3. Draw the segment OC that intersects the circles at D.
Step 4. Draw a perpendicular line to the parallel line that passes through point C. Label point E.
Step 5. Use centre point C and radius r. Draw an arc that links the points D and E.
Linking a circle and a straight line with an arc whose radius (q) is greater than the radius of the circle
Step 1. Draw a line parallel to AB at a distance q.Step 2. Use centre point F and a radius equal to the difference between q and p. Draw an arc that intersects the parallel line at point G.
Step 3. Draw the line FG that intersects the circles at H.
Step 4. Draw a perpendicular line to the parallel line that passes through point G. Label point J.
Step 5. Use centre point G and radius q. Draw an arc that links the points H and J
Linking two circles with an arc of a smaller radius
Step 1. Use centre point N and a radius equal to the sum of the radius n and r. Draw an arc.Step 2. Use centre point M and a radius equal to the sum of m and r. Draw an arc that intersects the previous arc at point A.
Step 3. Draw the rays A and MA. Where the lines intersect the circles, label the points B and C, respectively.
Step 4. Use centre point A and radius r. Draw an arc that links the points B and C.
Linking two circles with an arc of a greater radius
Step 1. Use centre point X and a radius equal to the difference between radius r and x. Draw an arc.Step 2. Use centre point Y and a radius equal to the difference between radius r and y. Draw an arc that intersects the previous arc at point Z.
Step 3. Draw the lines XZ and YZ. Where the lines intersect the circumferences, label the points P and Q, respectively.
Step 4. Use centre point Z and radius r. Draw an arc that links the points P and Q
