Q. 184.4( 9 Votes )

In ΔABC, AB = AC.

Answer :


Draw AEBC. Applying Pythagoras theorem in right-angled triangle AED,


Since, ABC is an isosceles triangle and AE is the altitude and we know that the altitude is also the median of the isosceles triangle.


So, BE = CE


And DE + CE = DE + BE = BD


AD2 = AE2 + ED2


AE2 = AD2 - ED2 …(i)


In ΔACE,


AC2 = AE2 + EC2


AE2 = AC2 –EC2 …(ii)


Using (i) and (ii),


AD2 - ED2 = AC2 –EC2


AD2 - AC2 = ED2–EC2


AD2 - AC2 = (DE + CE) (DE – CE)


AD2 - AC2 = (DE + BE) CD


AD2 - AC2 = BD.CD


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