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Tangent Theorem

Three tangent...

Question

Three tangents are drawn at random to a given circle . Find the probability of the tangents to 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.

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

The circle circumscribing the triangle formed by three tangents to a parabola passes through _____

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