Question

If two diameters of a circle intersect each other at right angles, then quadrilateral formed by joining their end points is a

(a) rhombus

(b) rectangle

(c) parallelogram

(d) square

Answer 1

(d) square

The given information in the form of the following figure is as follows:

Since, four sides of the quadrilateral ACBD are four chords which subtend equal angles at the centre. Therefore,

(Since AB and CD are perpendicular diameters)

So sides AC, BC, BD and AD are equal, as equal chords subtend equal angle at the centre.

So , AC = CB = BD = DA …… (1)

We know that diameters subtend an angle of measure 90° on the circle.

So, …… (2)

From (1) and (2) we can say that is a square.

Hence, the correct answer is option (d).