To find the probability that a randomly selected point within the circle falls in the red-shaded triangle, we can compare the area of the red-shaded triangle to the total area of the circle.
First, calculate the area of the circle using the formula A = πr^2, where r is the radius of the circle. Since the diameter of the circle is 12 cm, the radius is half of that, so r = 6 cm.
A = π(6 cm)^2
A = 36π cm^2
Now, calculate the area of the red-shaded triangle. Since the triangle is isosceles with two sides of 12 cm each, and the angle between them is 90 degrees, it can be considered as a right-angled triangle.
The area of a right-angled triangle can be calculated as A = 1/2 * base * height. In this case, the base and height of the triangle are both 12 cm.
A = 1/2 * 12 cm * 12 cm
A = 72 cm^2
Now, to find the probability of a randomly selected point falling in the red-shaded triangle, divide the area of the red-shaded triangle by the area of the circle:
P = (Area of red-shaded triangle) / (Area of circle)
P = 72 cm^2 / 36π cm^2
P ≈ 0.64
So, the probability that a randomly selected point within the circle falls in the red-shaded triangle is approximately 0.64 or 64%.
