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I'm not sure whether you are asking what convex means, or to prove that all circles are convex. A shape is convex if all pairs of points within it (i.e., the interior, not just the boundary) have all points between them within the shape. That is, if you draw the straight line segment between 2 points on or within a circle, all points of that line segment are within the circle.
To prove that, you could use Euclid's axioms of geometry, or analytic geometry, which deals with the coordinates of points and the equations they satisfy. I will leave the proof as an exercise, since it is rather involved (but not necessarily advanced) and I don't know if that is what you are asking for anyway!
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∙ 11y ago
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Is a regular circle concave or convex?
convex
Is a circle a convex set?
no
Region enclosed by a circle a convex set?
Yes.
How many vertexes in circle?
None. Circles are convex shapes without straight sides and so there are no vertices (the correct plural of vertex).
Is a ploygon convex or not convex?
a polygon is convex
Is a regular circle concave or convex?
convex
Is a circle a convex set?
no
Region enclosed by a circle a convex set?
Yes.
What type of polygon is found in a geometry circle?
Convex Polygon
How is a triangle and a circle similar?
A closed, convex, plane (2-dimensional) shape.
What attribute has a rectangle circle and triangle?
All three are convex plane figures.
Is there a shape made up of segments that is not a polygon?
A circle, semicircle, segments or sectors of circle, ellipse, segments or sectors of ellipses, cardiods, closed convex wriggly shapes.
How many vertexes in circle?
None. Circles are convex shapes without straight sides and so there are no vertices (the correct plural of vertex).
What is the use of the newton's rings?
newtons ring is formed due to the consequtive circle of different radius of bright and dark in which the centre is dark
Is a ploygon convex or not convex?
a polygon is convex
Difference of non convex and convex?
A non convex is a concave and a convex is differently shaped
Is a circle concave or convex?
This depends on your definition. One could say that circles ({p in R^n : d(p,m) = r}) are concave, while (open) disks ({p in R^n : d(p,m) < r}) are convex.
