If a parallelogram is inscribed in a circle, then it must be a Rectangle
What is a parallelogram?
Any quadrilateral in which opposites sides are parallel is called a parallelogram.
What is a triangle?
Any 2 dimensional figure bounded by 3 sides and sum of all the angles is 180° is called a triangle.
What is a rhombus?
A parallelogram with four equal sides and sometimes one with no right angles is called a rhombus.
What is a rectangle?
A rectangle is a four sided quadrilateral, having all the internal angles equal to 90 degrees and opposite sides are equal.
What is a trapezoid?
A trapezoid is a quadrilateral with one pair of opposite sides parallel.
How to know what the parallelogram will be if it is inserted in a circle ?
- We know that if a quadrilateral is inscribed in a circle then the sum of its opposite sides will be supplementary (180°)
- We know that all the angles of a rectangle is 90°. So sum of opposite angles will be 180°.
This follows the characteristics features of a circle.
So the required parallelogram will be a rectangle.
Option C is correct.
- In rhombus and trapezoid the sum of opposite angles are not 180°.
- A triangle is not a parallelogram.
So, options A , B, D are incorrect.
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