Multiple choice

The chord of contact of tangents from three points $A, B, C$ to the circle $x^2 + y^2 = a^2$ are concurrent, then A, B, C will

  1. Be concyclic

  2. Be collinear

  3. Form the vertices of a triangle

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The chord of contact of a point (x1, y1) with respect to x^2 + y^2 = a^2 is xx1 + yy1 = a^2. If the chords of contact for three points are concurrent, the points themselves must lie on a line (the polar line of the point of concurrency).

AI explanation

The chord of contact of tangents drawn from a point to a circle represents the polar line of that point with respect to the circle. If the polars of three points are concurrent at a specific point, then the original three points must lie on the polar of that specific concurrent point, which forms a straight line. Therefore, points lying on the same straight line are collinear.

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