Answer :

Given: ABC is a right angled triangle with A = 90°



To prove: BQ2 + PC2 = BC2 + PQ2


Proof:


By applying Pythagoras theorem in ΔAPQ, we get,


PQ2 = AP2 + AQ2 ……………… (1)


By applying Pythagoras theorem in ΔABQ, we get,


BQ2 = AB2 + AQ2 ……………… (2)


By applying Pythagoras theorem in ΔAPC, we get,


PC2 = AP2 + AC2 ………………… (3)


By applying Pythagoras theorem in ΔABC, we get,


BC2 = AB2 + AC2 ……………… (4)


By adding (1) and (2) we get,


BQ2 + PC2 = AB2 + AQ2 + AP2 + AC2


BQ2 + PC2 = AB2 + AC2 + AQ2 + AP2


Substituting from (1) and (4) we get,


BQ2 + PC2 = BC2 + PQ2


Hence proved.


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