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The chords of contact of tangents from three points `A ,Ba n dC`to the circle `x^2+y^2=a^2`are concurrent. Then `A ,Ba n dC`willbe concyclic(b) be collinearform the vertices of a trianglenone of theseA. be concyclicB. be collinearC. form the vertices of a triangleD. none of these |
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Answer» Correct Answer - 2 Let the coordinates of A,B, and C be `(x_(1),y_(1)),(x_(2),y_(2))` and `(x_(3),y_(3))` , respectively. Then, the chords of contact of tangents drawn from A,B, and C are `x x_(1)+y y_(1)= a^(2), x x_(2)+y y_(2) =a^(2), ` and `x x _(3)+y y_(3)=a^(2)`, respectively. These three lines will be concurrent , if `|{:(x_(1),y_(1),-a^(2)),(x_(2),y_(2),-a^(2)),(x_(3),y_(3),-a^(2)):}|=0` or `|{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=0` Therefore, points `(x_(1),y_(1)),(x_(2),y_(2))` and `(x_(3),y_(3))` are collinear. |
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