GEO: Relationships, Semicircle, Arcs - Quick Questions

[EggNest]

I was wondering if anyone could help me with the following...


Relationships between radii, diameters, and chords of a circle.

Why are three points needed to name a semicircle (half circle)?

Difference between arc measure and arc length for a minor arc?

 

[nolachrymose]

Well, a chord is a segment whose endpoints lie on the circumfrence of the circle. A diameter is a special chord which passes through the center of the circle, and the radius is a segment drawn from the center of the circle to any point on the circle, with its measure being always half that of the diameter.

I'm not quite sure why you need three points to name a semicircle, but I'd imagine it would be to distinguish it from a minor arc. I would guess it's because the third point helps distinguish which semicircle of the full circle is being referred to.

Arc measure is an angular measurement (usually in degrees in geometry, and radians in calculus and trigonometry), while arc length is the actual length of the curvature (i.e. as if you were to walk along the arc, what distance is traversed).