How do you prove that rhombus inscribed in a circle is a square?

To prove rhombus inscribed in a circle is a square,we need to prove that either any one of its interior angles is equal to 90° or its diagonals are equal. In the figure,diagonal BD is angular bisector of angle B and angle D. Hence, rhombus inscribed in a circle is a square.

How do you prove a rhombus is a square?

Proving that a Quadrilateral is a Square If the quadrilateral is a rhombus one of whose angles is a right angle, then it is a square. If the quadrilateral is a rhombus with congruent diagonals, then it is a square.

What must be true about a rhombus that is inscribed in a circle?

A quadrilaterals opposite angles must add up to 180 in order to be inscribed in a circle, but a rhombuses opposite angles are equal and do not add up to 180. Therefore, a rhombus that does not have 4 right angles cannot be inscribed in a circle.

Can a circle be inscribed in a rhombus?

Circle inscribed in a rhombus touches its four side a four ends. The side of rhombus is a tangent to the circle. Here, r is the radius that is to be found using a and, the diagonals whose values are given.

How do you prove that the parallelogram circumscribing a circle is a rhombus?

AB + CD = AD + BC. Since ABCD is a parallelogram, we have AB = CD and AD = BC (Because opposite sides of a parallelogram are equal). Hence AB = AD. Hence ABCD is a rhombus.

How do you prove a rhombus?

To prove a quadrilateral is a rhombus, here are three approaches: 1) Show that the shape is a parallelogram with equal length sides; 2) Show that the shape’s diagonals are each others’ perpendicular bisectors; or 3) Show that the shape’s diagonals bisect both pairs of opposite angles.

Why rhombus Cannot be inscribed in a circle?

1 Expert Answer In general a rhombus has two diagonals that are not equal (except a square) and therefore the endpoints of the shorter diagonal would not be points on the circle. Unless the rhombus is a square, it can’t be inscribed in a circle.