Question

1
PQRS is a rhombus and the diagonals PR and SQ intersect at O. Prove that OP square plus OR square equals PS square plus SR square minus half is Q square

Answer 1

Answer:

Step-by-step explanation:

n triangle POQ,

OP + OQ > PQ __(1)

Since sum of two sides is greater than 3rd sides.

In triangle QOR,

OQ + OR > QR ___(2)

Since sum of two sides is greater than 3rd sides.

In triangle SOR,

OS + OR > RS ___(3)

Since sum of two sides is greater than 3rd sides.

In triangle POS,

OP + OS > PS ___(4)

Since sum of two sides is greater than 3rd sides.

On adding all 4 equations we get,

OP + OQ + OQ + OR + OR + OS + OS + OP > PQ + PR + RS + PS

( OP + OR ) + ( OP + OR ) + ( OQ + OS ) + ( OQ + OS ) > PQ + PR + RS + PS

PR + PR + QS + QS > PQ + PR + RS + PS

PQ + PR + RS + PS > 2 (PR+QS)