Question

Statement I The chord of contact of tangent from three points A, B and C to the circle `x^2+y^2=a^2` are concurrent, then A, B and C will be collinear. Statement II A, B and C always lie on the normal to the circle `x^2+y^2=a^2`.
A. be concyclic
B. be collinear
C. form the vertices of a triangle
D. none of these

Answer 1

Correct Answer - B
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`
`rArr-a^(2)|(x_(1),y_(1),1),(x_(2), y_(2),1),(x_(3), y_(3),1)|=0rArr |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|=0`,
Which is the condition of collinearity of points A, B, C.