In each picture below, the explanation of the green part is given. Calculate in each, the probability of a dot put without looking to be within the green part.
A square with all vertices on a circle.
The figure is shown below:
Let the side of square be x
AC is the diameter of the circle as well as the diagonal of the square.
In Δ ABC
We know that, AB = BC (side of the square)
⇒ AB2 + BC2 = AC2 (Pythagoras theorem)
⇒ AB2 + AB2 = AC2
⇒ x2 + x2 = AC2
⇒ 2x2 = AC2
⇒ √2 x = AC
Area of green region = Area of square = 4 × side
Area of green region = 4 × x
= 4x
Area of total region = Area of circle = πr2
Area of total region = π × (√2x)2 = 2πx2
Probability of getting dot inside green region
= 
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.
