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Radius and Tangents of a Circle Are Perpendicular

4. Three tang...

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4. Three tangents are drawn at random to a given circle. Find the probability that the tangents form a triangle.

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Q. A pair of tangents are drawn from origin to the circle

x^{2} + y^{2} - 8 x + 12 = 0

. Another tangent is drawn to this circle such that this circle will become the incircle of the triangle which is formed by these three tangents. What will be the area of the triangle formed?

Q. A pair of tangents are drawn from origin to the circle

x^{2} + y^{2} - 8 x + 12 = 0

. Another tangent is drawn to this circle such that this circle will become the incircle of the triangle which is formed by these three tangents. What will be the area of the triangle formed?

Q. Three triangles are drawn at random to a given circle: show that the odds are

3

1

against the circle being inscribed in the triangle formed by them.

Q. Show that three circles can be drawn to touch a parabola and also to touch at the focus a given straight line passing through the focus, and prove that the tangents at the point of contact with the parabola form an equilateral triangle.

P Q, P R

are drawn to the circle

x^{2} + y^{2} = a^{2}

from a given point

P

. Find the equation of the circum-circle of the triangle

P Q R

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