tmua 2022 Q19

tmua · Uk · paper2 1 marks Proof Proof of Equivalence or Logical Relationship Between Conditions

A polygon has $n$ vertices, where $n \geq 3$. 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?
A no values of $n$
B $n = 3$ only
C $n = 3$ and $n = 4$ only
D $\quad n = 3$ and $n \geq 5$ only
E all values of $n$

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A polygon has $n$ vertices, where $n \geq 3$. It has the following properties:

\begin{itemize}
  \item Every vertex of the polygon lies on the circumference of a circle $C$.
  \item The centre of the circle $C$ is inside the polygon.
  \item The radii from the centre of the circle $C$ to the vertices of the polygon cut the polygon into $n$ triangles of equal area.
\end{itemize}

For which values of $n$ are these properties sufficient to deduce that the polygon is regular?\\
A no values of $n$\\
B $n = 3$ only\\
C $n = 3$ and $n = 4$ only\\
D $\quad n = 3$ and $n \geq 5$ only\\
E all values of $n$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20