What is the probability that a triangle formed by three random points?

What is the probability that the triangle with vertices at these three points contains the center of the circle? Answer: 50\%.

What is the probability of the triangle formed by any 3 points on the circumference of a circle to contain the center of the circle?

1/4
The probability that the interior of the triangle determined by the three points picked at random on the circumference of a circle contains the origin is 1/4.

What is the average area of a triangle?

So, the area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle. Example: Find the area of the triangle. The area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle.

What is the probability that three random points on a unit circle would form a triangle that includes the center of the unit circle?

There is a 1/4 chance that point C will fall in place to create a triangle which contains the center of the circle.

What is the total area of the three triangles?

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

How many circles contain all the three points ABC?

Only 1 Circle containing all the three non collinear points A, B, C. There can only be one circle such that it contains all three non-collinear points.

What’s the probability that you randomly choose three points on a circle and these three points would be covered by a semi circle?

There are 3 points, thus three semi circles and the events that the all the points lie on a semi circle starting at each of the points are mutually exclusive. Therefore the probability is 3×122.

What is the average area of the triangle ABC?

Since the three points are chosen independently, the average area of the triangle ABC is: 3 2 π ≈ 0.47746. Since the answers from Alex Eustis and Klaus Grünbaum don’t agree, I decided to go ahead and write (what I regard as) a convincing Monte Carlo simulation which averages 10,000 areas on each run.

What is the probability that a triangle can be put together?

Point is uniquely and randomly determined by the two break points. If the points are distributed uniformly and chosen independently, the probability that a triangle can be put together from the three pieces is The stick is first broken into two pieces. The longest (or rather, not the shortest) is then broken into two.

What is the central angle of AB on the unit circle?

The diagram above shows three randomly chosen points A, B, C on the unit circle. We choose a coordinate system so that the chord AB is perpendicular to the x-axis. The chord AB makes a central angle of 2 α, and the point C makes an angle of θ with the positive x-axis.