Show that rectangle is the only parallelogram that can be inscribed in a circle. Class 9

Show that rectangle is the only parallelogram that can be inscribed in a circle. Class 9

Question 1.

Show that rectangle is the only parallelogram that can be inscribed in a circle. Class 9

Solution:

Given: Parallelogram ABCD is cyclic.

To Show: ABCD is a rectangle.

Proof.

ABCD is a parallelogram. ... [Given]

∴ ∠B = ∠D

...(i)[Opposite angles of a parallelogram]

Also, ABCD is a cyclic quadrilateral

... [Given]

∴ ∠B + ∠D = 180° ...[Opposite angles of a cyclic quadrilateral]

∴ ∠B + ∠B = 180° ...[From (i)]

∴ 2∠B = 180°

∴ ∠B = 90°

∴ ∠B = ∠D = 90° ...[From (i)]

Similarly, we can prove that, ∠A = ∠C = 90°.

∴ ABCD is a rectangle.