A Tangent Chord and a Tangent Circumcircle

★ 8/10Tangent Circle conic sections analytic geometry Vieta's Formulas

Problem

Consider the parabola $y=x^2$ and the circle $P:x^2+(y-2)^2=1$ . From a point $A$ on the parabola, the two tangent lines to the circle meet the parabola again at points $B$ and $C$ ; join $BC$ .

1. Prove that the line $BC$ is tangent to the circle $P$ . 2. Prove that the circumscribed circle of $\triangle ABC$ is tangent to the line $y=0$ .

Answer

Solution

Difficulty	8/10
Topics	Tangent Circle, conic sections, analytic geometry, Vieta's Formulas

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