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Beijing normal university printing plate volume 1 mathematics problems second day
Using Pythagorean Theorem:

In triangle ABD and triangle ADC respectively.

AB2=BD2+AD2 ( 1)

AC2=AD2+CD2 (2)

( 1)- (2)

AB2-AC2 = BD2+AD2-AD2-CD2 = BD2-CD2 =(BD+CD)(BD-CD)(3)

BD+CD=BC (4)

According to (3)\(4), AB2-AC2=BC(BD-CD).

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