Solution pls

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Hey so this is my first post so Im not really sure how this goes but basically for this question, you need to have the prior knowledge that when there is a right angle triangle the area will be the greatest than from any other degree. So when the first point on the semi circle and the 4th point make a triangle it is a right angle triangle. And so when we find the area of this we get x as the area of the triangle. (1/2*square root 2x*square root 2x as the radius is square root 2x) we can then see that for thr area of the triangle to be less than x we need it to not be a right angle triangle. As point 1 on the semi circle and point 7 cant even make a triangle, there are 5 different triangles to be made by each point out of which 1 triangle will have an area x. So the probability of a triangle being less than x is 4/5

it is quite arduous task to solve this one but we can guess this particular question without any knowledge
total triangle form from centre and two points are 7c2 -1(the diameter)=20
so 20 in denominator and only viable option which has factor of 20 is A

Area of semi circle is xπ so πr2/2 = xπ

r =√2x

A triangle has its maximum area when the two sides are perpendicular

1/2 x √2x x √ 2x

so the max area is x, which is a right-angled triangle.


Since the points have equal distance apart, angle between them will be the same. Let that angle be a.


6a = 180

a = 30

Now total number of triangles = 7C2 = 21- 1 = 20

We removed one because the points on the diameter cant form a triangle.

To find the desired outcome we remove all the number of right-angled triangles so the areas of each of the remaining will be less than x


Which gives 16

So probability = 16/20 = 4/5.