Demonstrate that the diagonals of a rectangle inscribed in a circle pass through the centre of the circle.
Explanation:
Given, \(PQRS\) is a rectangle inscribed in a circle.
Let the diagonals \(PR\) and \(QS\) intersect at the point \(O\).
\(OP=\) and \(OQ =\) []
This implies, \(O\) is the .
Also, we know that, every angle in a rectangle is \(^\circ\).
Since, the rectangle is inscribed in a circle, the diagonals \(PR\) and \(QS\) are the of the circle.
So, the chords \(PR\) and \(QS\) subtends a at the circumference.
Thus, the diagonals \(PR\) and \(QS\) are the of the circle. [Since, ]
Therefore, the point \(O\) is the of the circle.
Therefore, the diagonals of the rectangle \(PQRS\) intersect at the centre.