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A cyclic rhombus is a 

A) Rectangle 

B) Square 

C) Parallelogram 

D) Trapezium

2 Answers

+1 vote
by (57.0k points)
selected by
 
Best answer

Correct option is (B) Square

A cyclic parallelogram is a rectangle.

Hence, a cyclic rhombus is a square.

Alternative method :-

Let ABCD is a cyclic rhombus.

\(\therefore\) \(\angle A+\angle C\) \(=180^\circ\) and

\(\angle A=\angle C\)

\(\Rightarrow\) \(2\angle A\) \(=180^\circ\)

\(\Rightarrow\) \(\angle A\) \(=\frac{180^\circ}2=90^\circ\)

Since, if an angle in a rhombus is \(90^\circ\) then it becomes square.

\(\therefore\) ABCD is a square.

+1 vote
by (38.9k points)

Correct option is  B) Square

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