MathDB

Six different points

A, B, C, D, E, F

are marked on the plane, no four of them lie on one circle and no two segments with ends at these points lie on parallel lines. Let

P, Q,R

be the points of intersection of the perpendicular bisectors to pairs of segments

(AD, BE)

(BE, CF)

(CF, DA)

respectively, and

P', Q' ,R'

are points the intersection of the perpendicular bisectors to the pairs of segments

(AE, BD)

(BF, CE)

(CA, DF)

respectively. Show that

P \ne P', Q \ne Q', R \ne R'

, and prove that the lines

PP', QQ'

and

RR'

intersect at one point or are parallel.

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