A point is taken inside the circle circumscribed about a right-angled triangle with legs 6 and 8.

A point is taken inside the circle circumscribed about a right-angled triangle with legs 6 and 8. Find the probability that it lies inside the triangle.

1) The probability of a point falling into a triangle is a point falling into the area of a triangle. You need to find the area of this triangle and compare with the area of the circle.

2) The radius of the circumscribed circle R = D = c / 2, where c is the hypotenuse. Determine the hypotenuse c along legs 6 and 8.

c ^ 2 = 6 ^ 2 + 8 ^ 2 = 36 = 64 = 100. Radius R = D / 2 = √100 / 2 = 10/2 = 5;

3) Area of a circle: C = 3.14 * R ^ 2 = 3.14 * 5 ^ 2 = 3.14 * 25 = 78.5.

4) Area of a triangle c = 6 * 8/2 = 48/2 = 24;

5) Probability p = (s / C) * 100% = (24 / 78.5) * 100% = 30.5%