In ∆ Abc, Ad ⊥ Bc. Prove That Ac2 = Ab2 +Bc2 − 2bc X Bd - Mathematics

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Sum

In ∆ ABC, AD ⊥ BC.
Prove that  AC2 = AB2 +BC2 − 2BC x BD

In ∆ ABC (Figure 3), AD ⊥ BC.
Prove that  AC2 = AB2 +BC2 − 2BC x BD

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Solution

Applying Pythagoras theorem in ΔADB, we obtain

AD2 + DB2 = AB2

⇒ AD2 = AB2 − DB2                                               .....(1)

Applying Pythagoras theorem in ΔADC, we obtain

AD2 + DC2 = AC2

AB2 − BD2 + DC2 = AC2    ...[Using equation (1)]

AB2 − BD2 + (BC − BD)2 = AC2

AC2 = AB2 − BD2 + BC2 + BD2 −2BC x BD

AC2 = AB2 + BC2 − 2BC x BD

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2018-2019 (March) 30/4/3

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