MathematicsHard19×since 2002Q5032Two vertices of a triangle ABC\mathrm{ABC}ABC are A(3,−1)\mathrm{A}(3,-1)A(3,−1) and B(−2,3)\mathrm{B}(-2,3)B(−2,3), and its orthocentre is P(1,1)\mathrm{P}(1,1)P(1,1). If the coordinates of the point C\mathrm{C}C are (α,β)(\alpha, \beta)(α,β) and the centre of the of the circle circumscribing the triangle PAB\mathrm{PAB}PAB is (h,k)(\mathrm{h}, \mathrm{k})(h,k), then the value of (α+β)+2( h+k)(\alpha+\beta)+2(\mathrm{~h}+\mathrm{k})(α+β)+2( h+k) equalsA81B15C51D5Check answerSkip