Question

as shown in figure, a, b, c and d are the centres of four congruent circles the diameter is 14 cm if a point from quadrilateral ABCD is selected such that it does not lie on the circle then find its probability

Answer 1

In the figure above, the radius of the circle with center O is 1 and BC = 1. ... Since AC is the diameter and B is a point on the circle, triangle ABC is a right angled

Answer 2

Given: A, B, C, and D are the centers of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD

To find: Probability that the point will be chosen from the shaded region,

In the figure we can see 4 circles of radius 1 unit.



Area of quarter circle with centre A:



Since all the circles are of the same radius hence the area of quarter with centre B, C, D will be same as the area of circle of quarter of circle with centre A.

Hence total area covered by 4 quarter circle will be



Side of the square will be 2 units

Area of square ABCD=4 unit2

Area of the shaded portion 

We know that PROBABILITY



Hence probability of the shaded region is