∑ Mathematics LabTriangles and Notable Centers · v4.0.4

MATHEMATICS LAB · GEOMETRY

Triangles and Notable Centers

Build triangles with three draggable vertices and explore medians, altitudes, angle bisectors, perpendicular bisectors, notable centers, incircles, and circumcircles.

Coordinates are real numbers and measurements use arbitrary units (u). For degenerate configurations, the lab reports undefined constructions instead of inventing results.

1. Vertex coordinates

Drag vertices on the graph or enter their coordinates
Point A
Point B
Point C
Examples:

Display options

Controls and information

Drag A, B or C. Use + and − or the mouse wheel to zoom; Fit centers the construction. On touchscreens, drag a vertex with one finger. You can also edit its coordinates using the fields.

2. Interactive construction

Equal scale on both axes
Dynamic geometric constructionCartesian plane with three draggable vertices: A, B and C. Coordinates can also be changed in the input fields.

3. Results

Updated values

4. How to construct notable centers

Three lines meeting at one point

5. Explained calculations

Formulas and numerical substitutions

What you can study in this version

Points and segments

Distance between two points, midpoints, the line through two vertices, perpendicular projections, and point-to-line distances. Use the dedicated tool for two arbitrary lines.

Triangles and constructions

Medians, altitudes, angle bisectors and perpendicular bisectors, including intersections, perimeter, area, angles, and notable centers.

Circles

Incircle and circumcircle, tangency points, radii, perpendicular lines, equations, and Cartesian-plane constructions.

This tool focuses on points and triangles in the Cartesian plane. Use other Geometry Lab tools for polygons, conics and three-dimensional constructions. Results are double-precision numerical approximations, not substitutes for formal proofs.