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area of a triangle with two vertices in parabola

Source: 1999 Spanish Mathematical Olympiad P1

July 21, 2018

parabolaanalytic geometryarea of a triangletangentgeometryconics

Problem Statement

The lines

t

and

t'

, tangent to the parabola

y = x^2

at points

A

and

B

respectively, intersect at point

C

. The median of triangle

ABC

from

C

has length

m

. Find the area of

\triangle ABC

in terms of

m