Question

prove That a cyclic rhombus is a square ​

Answer 1

Answer:

But a square has not only all sides equal but also the measure of all interior angles are right angles. So, to show : any rhombus is a square, we need to show any angle of a rhombus is right angle. In the figure,diagonal BD is angular bisector of angle B and angle D. Hence, rhombus inscribed in a circle is a square.

Answer 2

Question :

prove That a cyclic rhombus is a square

Solution :

∴ ∠A + ∠C and ∠B + ∠D

( Opposite angle of rhombus is equal )

∠A + ∠C = 180°

( Opposite angle of Cyclic rhombus )

∴ ∠A + ∠A = 180°

➞ ∠A = 90°

And ∠B + ∠D = 180°

( Opposite angle of Cyclic rhombus )

∴ ∠B + ∠B = 180°

➞ ∠B = 90°

∴ ∠A = ∠B = ∠C = ∠D = 90°

Then all angle of rhombus is right angle then this is a square.