Answer

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**Hint:**Here, we need to find the kind of the given cyclic quadrilateral. We will use the property of an angle in a semi-circle to find the measures of the interior angles of the cyclic quadrilateral. Using the measures of the angles, we can determine the type of the quadrilateral.

**Complete step-by-step answer:**First, we will draw the required figure for the problem.

Here, O is the centre of the circle, AC and BD are the diameters of the circle, and the diagonals of the quadrilateral ABCD. ABCD is a cyclic quadrilateral.

Now, we can observe that the arc ADC and the diameter AC form a semi-circle.

The angle in a semi-circle is always a right angle. It is the angle formed by the diameter on any point on the semi-circle.

Therefore, we get

\[\angle ADC = 90^\circ \]

The arc ABC and the diameter AC form a semi-circle.

Therefore, we get

\[\angle ABC = 90^\circ \]

The arc BCD and the diameter BD form a semi-circle.

Therefore, we get

\[\angle BCD = 90^\circ \]

The arc BAD and the diameter BD form a semi-circle.

Therefore, we get

\[\angle BAD = 90^\circ \]

Therefore, in the cyclic quadrilateral ABCD, we have

\[\angle ADC = \angle ABC = \angle BDC = \angle BAD = 90^\circ \]

Since all the interior angles of the cyclic quadrilateral ABCD are right angles, the cyclic quadrilateral ABCD is a rectangle.

**Thus, the correct option is option (b).**

**Note:**The quadrilateral given in the question is a cyclic quadrilateral. A cyclic quadrilateral is that quadrilateral whose four vertices lie on a circle. The opposite interior angles of a cyclic quadrilateral are supplementary angles. In other words, the sum of the opposite interior angles of a cyclic quadrilateral is 180 degrees.

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