Prove that the circumcircle of a triangle formed by three tangents to a parabola passes through the focus of the parabola.
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Prove that the circumcircle of a triangle formed by three tangents to a parabola passes through the focus of the parabola.
Prove that the circumcircle of a triangle formed by three tangents to a parabola passes through the focus of the parabola.
Let the tangents be
try = x + atr2
where r = 1, 2 and 3. By Problem 1, the feet of the perpendiculars drawn from the focus of the parabola onto the three tangents (which are the sides of a triangle) are collinear on the tangent at the vertex. Hence, from the section ‘Pedal Line (or Simson’s Line)’ , the circumcircle of the triangle passes through the focus.