### 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 M_{C}, those at A and C meet at M_{B}, and the tangents at B and C meet at M_{A}.

What if applet does not run? |

Prove that

- M
_{A}lies on PQ, M_{B}on PR, and M_{C}on QR. - PQ is parallel the tangent at A, PR at B, and QR at C.

### Conic Sections > Parabola

- The Parabola
- Archimedes Triangle and Squaring of Parabola
- Focal Definition of Parabola
- Focal Properties of Parabola
- Geometric Construction of Roots of Quadratic Equation
- Given Parabola, Find Axis
- Graph and Roots of Quadratic Polynomial
- Greg Markowsky's Problem for Parabola
- Parabola As Envelope of Straight Lines
- Generation of parabola via Apollonius' mesh
- Parabolic Mirror, Theory
- Parabolic Mirror, Illustration
- Three Parabola Tangents
- Three Points on a Parabola
- Two Tangents to Parabola
- Parabolic Sieve of Prime Numbers
- Parabolic Reciprocity
- Parabolas Related to the Orthic Triangle

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