pqrs is a quadrilateral and o is a point inside it (other than the point of intersection of the diagonals),prove - Maths - Triangles

Question

pqrs is a quadrilateral and o is a point inside it (other than the
point of intersection of the diagonals),prove that(
op+oq+or+os)​ greater than(pr+qs)

Brijendra Pal · Accepted Answer

Hi, we know that in a triangle sum of two sides is greater than third so

(1) Now if we will join diagonals then in triangle PQR, QRS, RSP and PSQsum of two side is greater than third so PQ+QR>PRQR+RS>SQSR+PS>RPPS+PQ>SQadd all 2PQ+QR+RS+SP>2PR+SQPQ+QR+RS+SP>PR+SQputting this in above we get 2OP+OQ+OR+OS>PR+SQcorrect relation is this

pqrs is a quadrilateral and o is a point inside it (other than the point of intersection of the diagonals),prove that( op+oq+or+os)​ greater than(pr+qs)

pqrs is a quadrilateral and o is a point inside it (other than the point of intersection of the diagonals),prove that( op+oq+or+os) greater than(pr+qs)