Question 7 of 16advanced🔍 AnalyzeShort Answer2 marks

Is it possible to create a 4-sided shape other than a rectangle through this process?

Correct Answer

No, it is not possible to create a 4-sided shape other than a rectangle (or square, which is a special rectangle) through this process.

Reasoning: The diagonals of the quadrilateral are diameters of the circle. They always bisect each other at the center, which is a property of parallelograms. The angles subtended by diameters are always right angles. ∴ The shape must be a rectangle.

Exercise: Play with Circles | Q: 33 | (Page Page 10)
For More Understanding

Explanation

The chapter establishes that joining endpoints of diameters always creates a rectangle because the diagonals (diameters) bisect each other at the center, and angles in a semicircle are right angles. This guarantees all angles are 90°, making the quadrilateral a rectangle.

Solution Steps

  1. The diagonals of the quadrilateral are diameters of the circle.

  2. They always bisect each other at the center, which is a property of parallelograms.

  3. The angles subtended by diameters are always right angles.

  4. Therefore, the shape must be a rectangle.

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