Question

A square is inscribed in a circle. Which of the following statements are true? The diagonals are each twice the length of a side. The diagonals of the square are also diameters of the circle. The diagonals of the square intersect at the center of the circle. The diagonals form four congruent arcs.

Answer 1

false

true

true

true

lol

Answer 2

Options B, C and D

Explanation:

Given that a square is inscribed in a circle. This means that the circle passes through all the vertices of the square

Since angle of a square is 90 degrees and vertices lie on the circle, it follows that the diagonal of the square would be the diameter of the circle.

Also since each diagonal is a diameter of circle, the two diagonals intersect at centre of the circle

The diagonals being symmetrical and cutting at right angles have central angle divided into 4 equal portions of 90 degrees each

Hence diagonals form four arcs which have equal length

Hence right options are

Option B,C and D

OPtion A is wrong because diagonal will be square root of 2 times the side only