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Asymptotes

If the chord ...

Question

If the chord of contact of tangents from 3 points A,B,C to the Circle $x^{2} + y^{2} = a^{2}$ are concurrent, then A,B,C will be

be concyclic

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Be collinear

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Form the vertices of triangle

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None of these

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Solution

The correct option is B Be collinear
$x x_{1} + y y_{1} = a^{2}, x x_{2} + y y_{2} = a^{2} a n d x x_{3} + y y_{3} = a^{2} T h e s e l i n e s w i l l b e c o n u r r e n t ∣ ∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & - a^{2} x_{2} & y_{2} & - a^{2} x_{3} & y_{3} & - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0 ∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & - 1 x_{2} & y_{2} & - 1 x_{3} & y_{3} & - 1 \end{matrix} ∣ ∣ ∣ ∣ = 0$
Which is the condition to the collinearity of A,B,C.

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A, B, C

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