Question

Let abc be an isoceles triangle in which ab=bc and bd perpemdicular to ac then bd2-cd2=

Answer 1

Since, ADB is a right-angled triangle.

AD2 + BD2 = AB2

AD2 + BD2 = AC2 [given, AB = AC]

AD2 + BD2 = (AD + CD)2

AD2 + BD2 = AD2 + CD2 + 2AD.CD

[subtract AD2 from both sides]

BD2 = CD2 + 2AD.CD

[subtract CD2 from both sides]

BD2 - CD2 = 2AD.CD

Thus, BD2 - CD2 = 2AD.CD