In a rectangle, the diagonals are equal and bisect each other. Since the rectangle is cyclic, each diagonal is a diameter of the circle. Therefore, their intersection is the midpoint of a diameter, which is the centre.
Show that if a rectangle is inscribed in a circle, then the point of intersection of its diagonals must lie at the centre of the circle.
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Let ABCD be a rectangle inscribed in a circle. Its diagonals AC and BD are equal and bisect each other. Since AC and BD are equal chords passing through the centre, they are diameters of the circle. The diagonals of the rectangle intersect at their common midpoint. The centre of a circle is the midpoint of every diameter. Therefore, the point where the diagonals of the rectangle intersect must be the centre of the circle.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 I’m Up and Down and Round and Round (2026-27):
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