Prove that AB+DC=BC+AD
Answers
From this figure we can conclude a few points which are:
(i) DR = DS
(ii) BP BQ
(iii) AP = AS
(iv) CR = CQ
Since they are tangents on the circle from points D, B, A, and C respectively. Now, adding the LHS and RHS of the above equations we get,
DR+BP+AP+CR = DS+BQ+AS+CQ
By rearranging them we get,
(DR+CR) + (BP+AP) = (CQ+BQ) + (DS+AS)
By simplifying, AD+BC=CD+AB
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Answer:
Step-by-step explanation:
AP = AS _________________________EQ.1
BP = BQ_________________________EQ.2
CR = CQ_________________________EQ.3
DR = DS_________________________EQ.4
AP + BP = AB_____________________EQ.5
BQ + CQ = BC____________________EQ.6
CR + DR = CD_____________________EQ.7
AS + DS = AD_____________________EQ.8
Adding all equations, we get,
⇒ AP + BP + CR + DR = BQ + CQ + AS + DS
From equations 5,6,7 and 8
⇒ AB + CD = BC + AD ------------------------- HENCE PROVED