Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

Set $A=(0,0),B=(1,0),C=(1,1),D=(0,1),P=(x,0),Q=(1,y)$. If $\angle PDA={\theta }_1$ and $\angle CDQ={\theta }_2$, then $\tan {\theta }_1=x,\tan {\theta }_2=1-y$, and ${\theta }_1+{\theta }_2=45^{\circ }$. Hence $y=2x/(1+x)$. Then $(1-x{)}^2+y^2=(1+x-y{)}^2$, so $PB+BQ+PQ=(1-x)+y+(1+x-y)=2$.