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27. A circle ...

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27. A circle contain three points on its circumference they form a triangle. What is the probability that the tringle contains the centre.

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18

points are indicated on the perimeter of a triangle

A B C

(see figure). If three points are choosen probability that it will form a triangle.

Q. In a circle with centre

O

A, P, B

are three points on its circumference such that

P

is the mid-point of minor arc

A B

∠ A O B = θ

.

\frac{a r e a (△ A O B)}{a r e a (△ A P B)} = \sqrt{5} + 2

∠ A O B

2 θ

, then the ratio

\frac{a r e a (△ A O B)}{a r e a (△ A P B)}

Q. Points are selected at random inside the circle until a point is closer to the centre than to the circumference. What is the probability that exactly three points are selected?

Q. There is a point inside a circle,. What is the probability that this point is close to the circumference than to the centre?

Q. A given line segment is divided at random into three parts. What is the probability that they form sides of a possible triangle

?

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