In the quadrilateral abcd , prove that a b + bc + cd + d a greater than ac + bd
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ABCD is a quad.Its diagonals are AC and BD.
In triangle ACB, AB + BC > AC - 1
In triangle BDC, BC + CD > BD - 2
In triangle ACD, AD + DC > AC -3
In triangle BAD, AB + AD > BD -4
Adding 1,2,3 and 4,
AB + BC + BC + CD + AD + DC + AB + AD > AC + BD + AC + BD
2AB + 2BC + 2CD + 2AD > 2AC + 2BD
AB + BC + CD + AD > AC + BD.
Answered by
6
Answer:
ABCD is a quad.Its diagonals are AC and BD.
In triangle ACB, AB + BC > AC ......................(1)
In triangle BDC, BC + CD > BD .....................(2)
In triangle ACD, AD + DC > AC ...................(3)
In triangle BAD, AB + AD > BD ....................(4)
By Adding (1) (2) (3) and (4),
AB + BC + BC + CD + AD + DC + AB + AD > AC + BD + AC + BD
2AB + 2BC + 2CD + 2AD > 2AC + 2BD
AB + BC + CD + AD > AC + BD.
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