Diagonals PR and QS of a quadrilateral PQRS intersect each other at point O. Show that ar(△ OPQ)× ar(△ ORS)=ar(△ OPS)× ar(△ OQR).

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Similar questions

P Q R S

is a quadrilateral in which the diagonals intersect each other at O. Prove that

P Q + Q R + R S + S P < 2 (P R + Q S)

Q. In the given figure,

P Q R S

is a cyclic quadrilateral. Its diagonals

P R

and

Q S

intersect each other at

T

. If

∠ P R S = 80^{\circ} a n d ∠ R Q S = 50^{\circ}

, calculate

∠ P S R

Q. The diagonals PR and QS of a cyclic quadrilateral PQRS intersect at X. The tangent at P is parallel to QS. Prove that PR bisects

∠

QRS.

Q. PQRS is a quadrilateral in which diagonals PR and QS intersect at O. Prove that PQ + QR + RS + SP < 2 (PR + QS).

In Fig. PQRS is a quadrilateral in which diagonals PR and QS intersect in O. [4 MARKS]

Show that:
(i) PQ + QR + RS + SP $>$ PR + QS
(ii) PQ + QR + RS + SP $<$ 2 (PR + QS)

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