17.InÎABC, ADzBCprovethat AB2+CD2=BD2+AC2

1.	17.InÎABC, ADzBCprovethat AB2+CD2=BD2+AC2
Answer» ABD is a right angled traingle and AB is the hypotaneous (AB)^2 = (AD)^2 + (BD)^2 (AB)^2 - (BD)^2 = (AD)^2 ---------(i) now,ACD is also a right angled traingle (AC)^2 = (AD)^2 + (DC)^2 (AC)^2 - (DC)^2 = (AD)^2 ---(ii) (i) = (ii) (AB)^2 - (BD)^2 =(AC)^2 - (DC)^2(AB)^2 +(DC)^2 = (AC)^2 + (BD)^2

Answer»

ABD is a right angled traingle and AB is the hypotaneous

(AB)^2 = (AD)^2 + (BD)^2

(AB)^2 - (BD)^2 = (AD)^2 ---------(i)

now,ACD is also a right angled traingle (AC)^2 = (AD)^2 + (DC)^2 (AC)^2 - (DC)^2 = (AD)^2 ---(ii)

(i) = (ii)

(AB)^2 - (BD)^2 =(AC)^2 - (DC)^2(AB)^2 +(DC)^2 = (AC)^2 + (BD)^2

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