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A polygon which has a circumscribed circle is called a cyclic polygon.
All regular simple polygons, all triangles and all rectangles are cyclic.
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What kind of polygon has all vertices lie on a circle?
It is a regular polygon as for example an equilateral triangle
Prove four vertices of pentagon are concyclic?
First make sure you understand that concyclic simply means the points lie on a common circle. We are not told it is a regular pentagon but we will assume it is. We could create pentagons that are not even convex and would not be concyclic.Let's start with a regular pentagon. You can split it up into 5 congruent triangles with the points meeting at the middle. Any side of one of these triangle is connected from each of the vertices of the pentagon to the center of the pentagon. Since all 5 triangles are congruent, this distance must be the same for each of the vertices. So, we see that each of the vertices is equidistant from a given point. Now if we drew a circle centered at that point with a radius equal to the distance between the point and any vertex, that circle would pass through all 5 vertices. Therefore any four ( really all 5), vertices of a regular pentagon are concyclic.A nice proof would use Ptolemy's theorem. I will place a line to an answers.com page that helps with that.Another solution:The pentagon has to be regular. Otherwise, the question is impossible to prove.Consider a regular polygon ABCDE.Take triangles BCD & ECDBC=ED (sides of a regular polygon are equal)CD=CD (common side)
What is a polygon where all diagonals lie on its interior?
A convex polygon.
What is the fewest vertices a polyhedron can have?
Four, as in a tetrahedron. Any three points lie in a plane, so if you only had three vertices they couldn't make a three-dimensional object.
What is a non-degenerate triangle?
A non-degenerative triangle has 3 vertices which does not lie on a stright line. i.e the are not collinear
A polygon whose vertices lie on a circle?
triangle
What kind of polygon has all vertices lie on a circle?
It is a regular polygon as for example an equilateral triangle
Is every triangle whose vertices lie on a circle is isoscles?
No.
What is a polygon in a circle if each of its vertices lie on the circle?
For any number greater than or equal to 3, a suitable polygon can be found.
A line segment whose end points lie on a circle is called?
chord
How do you find the radius of segmented circle?
Assuming all the vertices of the segmentation lie on the circle, then you can choose any three of them as the corners of a triangle circumscribed by the circle. The perpendicular bisectors of the sides of that triangle intersect at the center of the circle.
A segment with endpoints on a circle?
A chord is a line segment whose endpoints lie on a circle. A secant is a line (or line segment) that intersects a circle in two places, endpoints NOT on the circle.
Prove four vertices of pentagon are concyclic?
First make sure you understand that concyclic simply means the points lie on a common circle. We are not told it is a regular pentagon but we will assume it is. We could create pentagons that are not even convex and would not be concyclic.Let's start with a regular pentagon. You can split it up into 5 congruent triangles with the points meeting at the middle. Any side of one of these triangle is connected from each of the vertices of the pentagon to the center of the pentagon. Since all 5 triangles are congruent, this distance must be the same for each of the vertices. So, we see that each of the vertices is equidistant from a given point. Now if we drew a circle centered at that point with a radius equal to the distance between the point and any vertex, that circle would pass through all 5 vertices. Therefore any four ( really all 5), vertices of a regular pentagon are concyclic.A nice proof would use Ptolemy's theorem. I will place a line to an answers.com page that helps with that.Another solution:The pentagon has to be regular. Otherwise, the question is impossible to prove.Consider a regular polygon ABCDE.Take triangles BCD & ECDBC=ED (sides of a regular polygon are equal)CD=CD (common side)
What is a polygon where all diagonals lie on its interior?
A convex polygon.
Circle A has a radius of 3 m What is the length of the longest chord in circle A?
A chord of a circle is a line segment whose two endpoints lie on the circle. The diameter, passing through the circle's centre, is the largest chord in a circle. So the answer is 6 m
What does chord mean in math?
A chord of a circle is a geometric line segment whose endpoints both lie on the circumference of the circle. A secant or a secant line is the line extension of a chord.
Is boxes a polygon?
No, a polygon must be 2 dimensional and lie on a single plane.
