In Figure, ABC is a triangle in which ∠ABC > 90° and AD ⊥ CB produced. Prove that AC2= AB2+ BC2+ 2 BC.BD.

In fig., ABC is a triangle in which ABC > 90^o and AD CB produced. Prove  that AC^2 = AB^2 + BC^2 + 2 BC . BD .

Asked by Pragya Singh | 1 year ago |  72

1 Answer

Solution :-

By applying Pythagoras Theorem in ∆ADB, we get,

AB2 = AD2 + DB2…………… (i)

Again, by applying Pythagoras Theorem in ∆ACD, we get,

AC2 = AD2 + DC2

AC2 = AD2 + (DB + BC) 2

AC2 = AD2 + DB2 + BC2 + 2DB × BC

From equation (i), we can write,

AC2 = AB2 + BC2 + 2DB × BC

Hence, proved.

Answered by Abhisek | 1 year ago

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