If diagonals of a cylindrical quadrilateral are diameter of the circles through the vertices of the quadrilateral, prove that it is a rectangle.

Open in App

Solution

We know that angle in a semicircle is $90^{o}$
$∴ ∠ A B C = ∠ A D C = 90^{o}$
Similarly, $∠ D A B = ∠ D C B = 90^{o}$
So, in ABCD are angles are $90^{o}$
Thus, ABCD is a rectangle.
proved.

Suggest Corrections

Similar questions

Q. If diagonals of a cyclic quadrilateral are diameter of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

The diagonals of a quadrilateral ABCD are perpendicular to each other. Prove that the quadrilateral formed by joining the midpoints of its sides is a rectangle.

Q. Quadrilateral

A B C D

is a rectangle whose three vertices are

B (4, 0), C (4, 3)

and

D (0, 3)

. Find the length of its diagonals.

Q. The diagonals of a quadrilateral

A B C D

are perpendicular. Show that the quadrilateral, formed by joining the mid-points of its sides, is a rectangle.

Join BYJU'S Learning Program

If diagonals of a cylindrical quadrilateral are diameter of the circles through the vertices of the quadrilateral, prove that it is a rectangle.

We know that angle in a semicircle is 90o∴∠ABC=∠ADC=90oSimilarly, ∠DAB=∠DCB=90oSo, in ABCD are angles are 90oThus, ABCD is a rectangle.proved.

We know that angle in a semicircle is $90^{o}$
$∴ ∠ A B C = ∠ A D C = 90^{o}$
Similarly, $∠ D A B = ∠ D C B = 90^{o}$
So, in ABCD are angles are $90^{o}$
Thus, ABCD is a rectangle.
proved.