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  • D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE ^2 BD ^2 = AB ^2 + DE ^2

Q13   D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove thatAE^2 + BD^2 = AB^2 + DE^2.

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In \triangle ACE, by Pythagoras theorem,

AE^2=AC^2+CE^2..................1

In \triangle BCD, by Pythagoras theorem,

DB^2=BC^2+CD^2..................2

From 1 and 2, we get

AC^2+CE^2+BC^2+CD^2=AE^2+DB^2..................3

In \triangle CDE, by Pythagoras theorem,

DE^2=CD^2+CE^2..................4

In \triangle ABC, by Pythagoras theorem,

AB^2=AC^2+CB^2..................5

From 3,4,5 we get

DE^2+AB^2=AE^2+DB^2

 

 

 

 

 

 

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seema garhwal

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