Mathematics

Problem

If the vertices of

\Delta ABC

are

A(\cos\alpha, \sin\alpha)

B(\cos\beta, \sin\beta)

and

C(\cos\gamma, \sin\gamma)

, then the orthocentre of the triangle is (1)

((\cos\alpha + \cos\beta + \cos\gamma), (\sin\alpha + \sin\beta + \sin\gamma))

(2)

((\cos\alpha + \cos\beta + \cos\gamma), 2(\sin\alpha + \sin\beta + \sin\gamma))

(3) (0, 0) (4)

((2\cos\alpha + 2\cos\beta + 2\cos\gamma), (2\sin\beta + 2\sin\gamma + 2\sin\alpha))