Theorem of cyclic quadrilateral:
Answers
Answer:
Cyclic Quadrilateral Definition:
The definition states that a quadrilateral which is circumscribed in a circle is called a cyclic quadrilateral. It means that all the four vertices of quadrilateral lie in the circumference of the circle.
Cyclic Quadrilateral Theorems
There are 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.
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
