How to draw an exact semi-circle with the "Draw Arc" function

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How to draw an exact semi-circle with the "Draw Arc" function

georgesbasement
Solving a problem that no one has encountered in the archives:

In the middle of the night it came to me that there is another accurate way of drawing semi-circles, for example, at the opposite ends of a pair of parallel lines (the alternate to drawing the arc with the "Center, Point, Angles" method, which requires finding that center point beforehand):

Pick the "Draw Arc" function that uses three entry points. Set the first point at the end of one of the parallel lines, the second point above the straight line that would join the closest ends of the adjacent lines (and half-way between), and the third point at the closest end of the second line. However, before setting the third point at the closest end of the second of the two parallel lines, observe the angle between the two straight lines before they become the desired arc: To get your semi-circle, those two lines should form a right angle (90 degrees). After a few cycles of ""Undo" and "Do" you will learn how high to set the intermediate point.

The geometrical reason why this should always work is that you are inscribing a square inside the imaginary circle (on inscribing a right triangle - without its hypotenuse - inside the semi-circle.

The same reasoning works for drawing a quarter circle with this method, wherein the aiming angle between those temporary lines connecting the first, second and third setting points will be 135 degrees.

LibreCAD wants to start drawing the arc soon after your cursor passes the second set point in this process, so that you will have to imagine for yourself where that second line of the inscribed square would lie, connecting the end of the first line to the other end of the intended arc. It is important that the second point should lie along the bisector of the angle between the two lines to be connected by your arc.

Good luck !
georgesbasement