Three-Centered Arch I: Drawing with a String and Three Nails
The arch is made of three arcs of circles with centers at the solid green point and the two red points. The green string is attached at the lower green point (the first "nail") and the other end can be moved with the slider "green angle" around the two other fixed "nails" at the reddish points.[more]
In this Demonstration the width of the arch is always the same. You can mark an expected height of the arch with the red locator "height". Then you can select different positions of the green and red locators to reach this marked height. When you select approximately correct parameters this will be indicated on the top of the arch by a little red circle. In the "initial settings", the red locator and its mirror divide the width of the arch into three equal segments.[less]
Three-centered arches are often used as door or window arches. There are similar constructions for arches with four or five centers. The four-centered arch has a vertex at the highest point.
The mathematical background can be seen in the Demonstration "Three-Centered Arch II: Geometric Construction".