Question

P and Q are two points on the sides CA and CB respectively of ABC right angled at C. Prove that :AQ²+BP²=AB²+PQ²

Answer 1

Answer:

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By Pythagoras' Theorem,

AQ² = AC² + CQ²

BP² = BC² + CP²

AB² = AC² + BC²

PQ² = CP² + CQ²

So

AQ² + BP² = ( AC² + CQ² ) + ( BC² + CP² )

                 = ( AC² + BC² ) + ( CP² + CQ² )

                 = AB² + PQ²