D and E are points on the sides CA and CB respectively of a triangle A – InterviewSolution

InterviewSolution

1.	D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that `A E^2+B D^2=A B^2+D E^2`.
Answer» In`/_ABC` `AB^2=AC^2+CB^2-(1)` In`/_ACE` `AE^2=AC^2+CE^2-(2)` In`/_DCE` `DE^2=DC^2+CE^2(3)` In`/_DCB` `BD^2=DC^2+CE^2-(4)` adding equaiton 2 and 4 `AE^2+BD^2=AC^2+CE^2+DC^2+CE^2` From equation 1 and 3 `AE^2+BD^2=AB^2+DE^2`

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