Given Line AB, draw two arcs (red) AC & BD (AC=BD) and then draw a line (blue) at the points of intersection E & F.
Given Arc AB, draw two arcs (red) AC & BD (AC=BD) and then draw a line (blue) at the points of intersection.
Given Angle ABC, draw an arc (red) at any radius from the vertex at B, then draw two equal arcs (blue) at the points of intersection and then draw a line (green) from the vertex at B to the intersection of the blue arcs.
Given Line AB and Point C, draw an arc (red) of any radius that intersects AB at two points E & F; then draw two arcs (blue) EG & EF (EG=EF); and finally, draw a line (blue) at the points of intersection G to point C. CG is now perpendicular to AB.
Given Line AB and Point C, draw an arc (red) of any radius that intersects AB at two points D& E; then draw two arcs (blue) DF & EF (DF=EF); and finally, draw a line (blue) at the point of intersection F to point C. CF is now perpendicular to AB.
Given Line AB and Point C, draw an arc (red) of any radius that intersects AB at points C & D; then draw a line (blue) from point D throught the center of the (red) arc until it intersects the arc again at E; then draw a line (green) at the points of intersection E to point C. CE is now perpendicular to AB.
Given Line AB and Point C, draw an arc from Point C at any radius (2.41) intersecting Line AB at Point D. Repeat the (2.41) radius from Point D interssecting AB at Point E. At Ponit E draw a radius from Point C (1,18) and repeat the (1.18) at Point D intersecting the (2.41) radius at Point F. Now, draw a line from Point C to Point F.
Given Line AB and a specific distance (ex. 1.18), draw two arcs (red) at random points on Line AB; then draw a Line CD (blue) that is tangenet to each arc.
Given a distance From Point A to Point 1, draw four (4) arcs (red) equal to A1 to the right of Point 1 along a horizontal line. Label each arc 2, 3, 4, & 5. Draw an additional arc (red) equal to A1 to the left of Point A and label -1. From Point A ,draw an arc (blue) toward Point B equal to A5 (5 units). From Point 3, draw an arc (blue dashed) toward Point C equal to 3-1 (4 units). Now, draw lines from Point A and from Point 3 to the intersection of arcs B & C or Point D.
Given Line AB, bisect Line AB by drawing two arcs (red) at any radius at Points A & B that intersect at Points C & D. Next draw a vertical line (red) from Point A to E equal in length to an arc (red) at Point A at a radius equal to the bisection of Line AB. From Point B, draw a line (red dashed) through Point E and intersecting an arc (red) at Point F equal to an arc (red) from Point E to Pont A. Now draw an arc (blue) using Points A & B and equal to the distance from Point A to Point F. Point G, is the center of a circle (blue) that contains the pentagon. To finish the pentagon, draw arcs (green) equal to the length of line AB that intersect the circle (blue) at Points H & I. Point J is found by drawing two additional arcs (green) at Points H & I. Connect Points BH, HJ, JI & IA inclose the pentagon (violet).
Given Center Lines AB & CD, draw a circle of any radius and bisect the radial center line from the center of the circle to the edge of the circle to find the the mid-point I using TWO equal (red) Arcs EF& HG and a (red) perpendicular line from EH to FG. Next draw an Arc (blue) from Point J where the vertical center line CD intersects the circle to Point K on center line AB with a radius from Point I to Point J. Next draw an Arc (green) from Point K on the horizontal center line AB to the circle Point L with a radius from Point J to Point K. This radius can be marked on the opposite side of the circle Point P and then copied at Points M & N. The distance between Points M & N should be the same as the distances between Points J & L, L & M, J & P, P & N.
Given two Center Lines and a Circle of any diameter, draw TWO Arcs (red) at Points A & D that intersect the Circle at Points C & B and E & F. Now draw straight lines (blue) from A to C, C to E, E to D, D to F, F to B and B to A to complete the hexagon.
Given a Line AB of any length, begin by drawing a Line (red) from Point A at ANY angle at ANY length. Next, using a scale or a compass mark of the desired number of equal parts (red & violet) (8 in this example). From the last Point 8, draw a Line (blue) to Point B. Now, using TWO triangles draw additional lines (green) parallel to Line 8B at each of the remaining Points 7 thru 1. Line AB is now divided into 8 equal parts.
Given TWO parallel lines AB & CD at ANY distance apart, place a scale with the zero (0) mark on Line AB and the 5 unit mark on Line CD. Next mark points or dots at the 1, 2, 3 and 4 unit marks and draw lines (blue) parallel to AB & CD at each point or dot.
Given THREE random points A, B, & C, select a radius greater than the half of the distance between Points A & B and draw TWO equal intersecting Arcs (red). Draw TWO additional equal Arcs (red) between Points B & C. Next draw TWO straight lines (blue) through the intersections of the arcs. Finally, draw a Circle (green) with the center at the intersection of the TWO (blue) lines and the radius equal to the distance to A, B or C. ALL Points should be on the (green) circle.
Given a Circle of any diameter, draw TWO straight line (red) that intersect the circumference of the circle at Points A, B & C. Next bisect line AB (red) using TWO Arcs (blue) and a strainght line DE (green). THEN bisect line BC (red) using TWO Arcs (blue) and a strainght line GF (green). The Point H of intersection of the TWO (green) lines is the center of the circle.
Given two parallel lines AB and CD, draw a line (red) connecting the end of Line Ab at point B and the end of Line CD at point C. Next bisect Line BC (red) using two equal arcs (red) EF and GH. Then draw a straight line (blue) through the intersections of the arcs to find the midpoint of Line BC. Now, bisect each half of Line BC using Arcs KL & IJ as well as Arcs MN & OP and draw additional Lines (blue) at the points of intersection. Next, draw perpendicular lines (green) at Points B & C. The points of intersection between the (Green) Lines and the 2nd & 3rd (Blue) lines are the center points for the Arcs (violet) that begin at Points B & c and meet at the midpoint of Line BC.
