Question

state and prove cyclic therom​

Answer 1

Answer:

icant sorrrrryyyy..................

Answer 2

Answer:

There is two important theorems which prove the cyclic quadrilateral.

Theorem 1

In a cyclic quadrilateral, the sum of either pair of opposite angles is supplementary.

Proof: Let us now try to prove this theorem.

Given: A cyclic quadrilateral ABCD inscribed in a circle with center O.

Construction: Join the vertices A and C with center O.

Cyclic Quadrilateral 2

Cyclic Quadrilateral Theorems

The converse of this theorem is also true, which states that if opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic.

Theorem 2

The ratio between the diagonals and the sides can be defined and is known as Cyclic quadrilateral theorem. If there’s a quadrilateral which is inscribed in a circle, then the product of the diagonals is equal to the sum of the product of its two pairs of opposite sides.

If PQRS is a cyclic quadrilateral, PQ and RS, and QR and PS are opposite sides. PR and QS are the diagonals.

(PQ x RS) + ( QR x PS) = PR x QS