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Q.1. No tangent can be drawn from the point (5/2, 1) to the circumcircle of the triangle with vertices (1, ) (1, ) , (3,) . (1985  1 Mark)
Ans. T
Sol. The circle passes through the points and
Here line AB is parallel to yaxis and BC is parallel to xaxis, there ∠ABC = 90°
∴ AC is a diameter of circle.
∴ Eq. of circle is
(x – 1) (x – 3) +
⇒ x2 + y2 – 4x = 0 … (1)
Let us check the position of pt (5/2, 1) with. respect to the circle (1),
we get
∴ Point lies inside the circle.
∴ No tangent can be drawn to the given circle from point (5/2, 1).
∴ Given statement is true.
Q.2. The line x + 3y = 0 is a diameter of the circle x^{2} + y^{2} – 6x + 2y = 0. (1989  1 Mark)
Ans. T
Sol. The centre of the circle x^{2} + y^{2} – 6x + 2y = 0 is (3, – 1)
which lies on the line x + 3y = 0
∴ The statement is true.
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