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TOT 2004 Spring - Senior A-Level p5 common tangent circle and y = x^2

Source:

February 25, 2020
parabolacommon tangentcirclegeometrytangentTangents

Problem Statement

The parabola y=x2y = x^2 intersects a circle at exactly two points AA and BB. If their tangents at AA coincide, must their tangents at BB also coincide?
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