o is a point in the interior of triangle pqr , prove that op+oq+or is greater than (pq+1r+pr)
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Answers
Answered by
63
PQ < OP + OQ ( Sum of 2 sides of triangle is greater than 3)
PR < OP + OR ( Sum of 2 sides of triangle is greater than 3)
QR < OP + OR ( Sum of 2 sides of triangle is greater than 3)
NOW ON ADDING LHS AND RHS WE GET -
PQ+ AC + BC < OP + OQ + OP + OR
OQ+ ORPQ + PR + QR< 2OP + 2OQ + 2OR
PQ + PR + QR< 2(OP + OQ + OR)
FINAL ANS = 1/2(PQ + PR + QR) < OP + OQ + OR
HENCE PROVED
PR < OP + OR ( Sum of 2 sides of triangle is greater than 3)
QR < OP + OR ( Sum of 2 sides of triangle is greater than 3)
NOW ON ADDING LHS AND RHS WE GET -
PQ+ AC + BC < OP + OQ + OP + OR
OQ+ ORPQ + PR + QR< 2OP + 2OQ + 2OR
PQ + PR + QR< 2(OP + OQ + OR)
FINAL ANS = 1/2(PQ + PR + QR) < OP + OQ + OR
HENCE PROVED
Answered by
25
PQ < OP + OQ ( Sum of 2 sides of triangle is greater than 3)
PR < OP + OR ( Sum of 2 sides of triangle is greater than 3)
QR < OP + OR ( Sum of 2 sides of triangle is greater than 3)
NOW ON ADDING LHS AND RHS WE GET -
PQ+ AC + BC < OP + OQ + OP + OR
OQ+ ORPQ + PR + QR< 2OP + 2OQ + 2OR
PQ + PR + QR< 2(OP + OQ + OR)
FINAL ANS = 1/2(PQ + PR + QR) < OP + OQ + OR
HENCE PROVED
PR < OP + OR ( Sum of 2 sides of triangle is greater than 3)
QR < OP + OR ( Sum of 2 sides of triangle is greater than 3)
NOW ON ADDING LHS AND RHS WE GET -
PQ+ AC + BC < OP + OQ + OP + OR
OQ+ ORPQ + PR + QR< 2OP + 2OQ + 2OR
PQ + PR + QR< 2(OP + OQ + OR)
FINAL ANS = 1/2(PQ + PR + QR) < OP + OQ + OR
HENCE PROVED
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