SOLUTION: A pentagon is inscribed in a circle. What is a possible number of the pentagon's diagonals that can be diameters of the circle?

Question 328656: A pentagon is inscribed in a circle. What is a possible number of the pentagon's diagonals that can be diameters of the circle?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
a pentagon has 5 sides.

We are assuming regular pentagons (each side is equal and all central angles are the same).

It has 5 central angles.

Each central angle is equal to 360 / 5 = 72 degrees.

A circumscribed circle will have the same center as the pentagon.

In order for a diagonal of the pentagon to be a diameter of the circle, it must form a straight line through the center of the pentagon.

This means that multiples of each central angle must equal 180 degrees.

This doesn't happen with a pentagon because an angle of 72 cannot be divided equally into 180.

The answer is that the possible number of the pentagon's diagonals that can also be a diameter of the circumscribed circle is zero.

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