Show that if a rectangle is inscribed in a circle, then the point of intersection of its diagonals Class 9

Show that if a rectangle is inscribed in a circle, then the point of intersection of its diagonals Class 9

Question 1.

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. Class 9

Solution:

Given : ABCD is a rectangle inscribed in a circle

Diagonals AC and BD intersect at O

To Show:

Point O is the centre of the circle

Proof:

ABCD is a rectangle,

∴ AC = BD ... [diagonals are equal]

Also, diagonals of a rectangle bisect each other:

∴ AO = OC and BO = OD

∠A = ∠B = 90°

∴ AC and BD are diameters of the circle. ...[Angle inscribed in semicircle is 90°]

Similarly, BD is also a diameter

∴ Point O is the centre of the circle.