Mathematics
If in △ABC, AB > AC and AD ⊥ BC, prove that AB2 - AC2 = BD2 - CD2.
Pythagoras Theorem
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Answer
From figure,
In right angle △ADB,
By pythagoras theorem we get,
AB2 = AD2 + BD2 ……..(i)
In right angle △ADC,
By pythagoras theorem we get,
AC2 = AD2 + CD2 ……..(ii)
Subtracting (ii) from (i),
AB2 - AC2 = AD2 + BD2 - (AD2 + CD2)
AB2 - AC2 = BD2 - CD2.
Hence, proved that AB2 - AC2 = BD2 - CD2.
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