Question

In a quadrilateral ABCD AB = BC = BD find AC

Answer 1

Answer:

Since, the sum of lengths of any two sides in a triangle should be greater than the length of third side Therefore, In Δ AOB, AB < OA + OB ……….(i) In Δ BOC, BC < OB + OC ……….(ii) In Δ COD, CD < OC + OD ……….(iii) In Δ AOD, DA < OD + OA ……….(iv) ⇒ AB + BC + CD + DA < 2OA + 2OB + 2OC + 2OD ⇒ AB + BC + CD + DA < 2[(AO + OC) + (DO + OB)] ⇒ AB + BC + CD + DA < 2(AC + BD) Hence, it is proved.Read more on Sarthaks.com - https://www.sarthaks.com/106403/abcd-is-quadrilateral-is-ab-bc-cd-da-2-ac-bd