Solve this ?

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1 Answer
Dec 21, 2017

drawndrawn

Let /_QCD=alpha

/_PCB=beta

So /_PCQ=90^@-(alpha+beta)

Now for Delta QCD,/_QDC=90^@ and DC = 1unit
So DQ=DCtanalpha=tanalpha

And for Delta PCB,/_PBC=90^@ and BC = 1unit
So PB=BCtanbeta=tanbeta

Hence for DeltaAPQ

AQ=1-tanalpha

AP=1-tanbeta

and

PQ=sqrt((1-tanalpha)^2+(1-tanbeta)^2)

Given

AQ+AP+PQ=2

=>1-tanalpha+1-tanbeta+sqrt((1-tanalpha)^2+(1-tanbeta)^2)=2

=>sqrt((1-tanalpha)^2+(1-tanbeta)^2)=tanalpha +tanbeta

=>1-2tanalpha+tan^2alpha+1-2tanbeta+tan^2beta=tan^2alpha+tan^2beta+2tanalphatanbeta

=>1-tanalpha-tanbeta=tanalphatanbeta

=>tanalpha+tanbeta=1-tanalphatanbeta

=>(tanalpha+tanbeta)/(1-tanalphatanbeta)=1=tan45^@

=>tan(alpha+beta)=tan45^@

=>alpha +beta=45^@

Hence /_PCQ=90^@-(alpha+beta)=90^@-45^@=45^@