Three Points on a Parabola

Let three points A, B, C lie on a parabola with axis OO'. Let AA', BB', CC' be parallel to the axis. Form intersections

  P = AB ^ CC',
Q = AC ^ BB'
R = BC ^ AA'.

Let the tangents to the parabola at A and B meet at MC, those at A and C meet at MB, and the tangents at B and C meet at MA.


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Prove that

  1. MA lies on PQ, MB on PR, and MC on QR.
  2. PQ is parallel the tangent at A, PR at B, and QR at C.
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