In ΔABC, if AD ⊥ BC, then AB2 + CD2 is equal to

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In ΔABC, if AD ⊥ BC, then AB2 + CD2 is equal to

Options:

A . 2BD2

B . BD2 + AC2

C . 2AC2

D . None of these

Answer: Option B
According to question,
Given :
AD ⊥ BC
∴ In ΔADB
AB2 = BD2 + AD2
AD2 = AB2 - BD2 . . . . . . . . (i)
In ΔADC
AC2 = AD2 + CD2
AD2 = AC2 - CD2 . . . . . . . (ii)
Compare equation (i) and (ii)
AB2 - BD2 = AC2 - CD2
AB2 + CD2 = BD2 + AC2

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