Mathematics
Which of the following quadrilaterals is not always a cyclic quadrilateral?
square
rhombus
rectangle
an isosceles trapezium
Answer
Given,
ABCD is a rhombus.
In a rhombus,
All sides are equal, but angles are not necessarily equal to 90°.
Opposite angles of a rhombus are equal.
So,
∠A = ∠C and ∠B = ∠D
But,
∠A + ∠C ≠ 180° (always)
Hence, opposite angles of a rhombus are not always supplementary.
Therefore, a rhombus is not always a cyclic quadrilateral.
Hence, option 2 is the correct option.
Related Questions
Every cyclic parallelogram is a/an :
square
rhombus
rectangle
isosceles trapezium
An isosceles trapezium is always :
a parallelogram
a square
a rectangle
a cyclic quadrilateral
The quadrilateral formed by angle bisectors of a cyclic quadrilateral is :
cyclic
square
rectangle
parallelogram
In the given figure, O is the centre of the circle and ∠ACB = 30°. Then, ∠AOB = ?
15°
30°
60°
90°
