Nine-Point Circle

The nine-point circle passes through the side midpoints (blue circles), altitude feet (green diamonds) and vertex–orthocenter midpoints (purple squares). Select a family to inspect it. Altitude feet may lie on extended sides. Some construction points coincide in right-angled or equilateral triangles.

Its center N is halfway between circumcenter O and orthocenter H; its radius is half the circumradius. G is the centroid. The centers lie on the Euler line; in an equilateral triangle they coincide and no unique Euler line exists. Nearby labels are grouped with slashes.

After the first construction, valid edits update the drawing automatically. Edit A, B and C in the coordinate menu, or drag a yellow vertex. Singular or unsupported drag positions are skipped; numerical edits still report errors. Plain wheel scrolls the page; Ctrl/⌘ + wheel zooms about the view centre. Mouse dragging the background pans. Touching the background scrolls the page. Reset fits the visible construction and keeps all inputs. After a vertex drag, the view fits automatically unless you have zoomed or panned. SVG saves the current drawing with its mathematical parameters and resolved theme colors. Measurements contains the radius and centre coordinates. Only raw inputs and the selected construction choices persist, including invalid drafts; no drawing, measurement panel or view is restored after navigation or reload. Coordinates use one arbitrary length unit, within −10000…10000.