Question

the vertices of a parallelogram lie on a circle prove that the diagonals are equal​

Answer 1

AC = BD

Step-by-step explanation:

Parallelogram ABCD lies in the circle such that the vertices of the parallelogram lies on the circle

then

$\angle A = \angle C$..(1)

(opposite angles of the parallelogram area equal)

now , we know that the sum of  opposite angles of the cyclic quadrilateral is 180°

therefore,

$\angle A + \angle C = 180^\circ$

using equation (1)

$\angle C + \angle C = 180^\circ$

$2\angle C = 180\\\angle C = 90^\circ$

since , parallelogram with one angle 90° is a rectangle

and

In a rectangle , diagonals are equal

therefore , AC = BD

#Learn more:

Prove that at any four vertices of a regular hexagon lie on a circle.

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Answer 2

Answer:

Step-by-step explanation:

Parallelogram ABCD lies in the circle such that the vertices of the parallelogram lies on the circle

then

..(1)

(opposite angles of the parallelogram area equal)

now , we know that the sum of  opposite angles of the cyclic quadrilateral is 180°

therefore,

using equation (1)

since , parallelogram with one angle 90° is a rectangle