Matpic
mathematics, in pictures
Concept

Inscribed angle

The angle a chord subtends at a point of the circle, the same wherever on its arc that point sits.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as locus — the same set of essays touches all of them, so they are one junction rather than several.

120°60°ABPthe same chordat the apex: 60°at the centre: 120°one is half the other,wherever P is put

An angle that does not care where it stands

Fix two points on a circle and look at them from anywhere else on the far arc. The angle is the same from every one of those places, and it is exactly half the angle at the centre.

geometry · inscribed angle Hcentremidpoints of the sides · feet of the altitudes · midpoints up to Hall nine sit at 97.0 from the centre, which is half the 194.1 of the circle through thecornerschecked again on 240 further triangles, every one of which puts its own nine on onecircle

Nine points on one circle

Three midpoints, three feet of altitudes and three more midpoints. Nine points defined in three unrelated ways, on an arbitrary triangle, and all nine sit on one circle — checked here on two hundred and forty triangles as well as on the drawn one.

geometry · triangle centres

Named alongside it

The objects these essays reach for when they reach for this one.

CircleLocusAltitudeAngleCentral angleCounterexampleCyclic quadrilateralHypotenuseIncidenceInvariantIsosceles trianglePerpendicular bisector

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