TMUA Official 2022 Paper 2 · Question 19

A polygon has $n$ vertices, where $n\ge3$ . It has the following properties:

Every vertex of the polygon lies on the circumference of a circle $C$ .
The centre of the circle $C$ is inside the polygon.
The radii from the centre of the circle $C$ to the vertices of the polygon cut the polygon into $n$ triangles of equal area.

For which values of $n$ are these properties sufficient to deduce that the polygon is regular?

Ano values of

n

n=3

only

n=3

and

n=4

only

n=3

and

n\ge5

only

Eall values of

n

examday