This question is uploaded on Instagram on page "@gercekboss" on 8th of may 2020. I provided Instagram link of this question. Click here to go to that question.
Take a look at figure given below. Give it a try and when you are ready then watch the solution.
Semicircle with 3 internal lines are drawn and their lengths are given. We have to find diameter of semicircle. Easy looking Hard Math Puzzle.
By cosine rule and Pythagoras theorem
Now apply cosine rule in triangle (1) at angle 90+θ (I written 90-θ in diagram)
Lets join 1st and 3rd point of this figure.
Now take a angles θ and 90+θ as shown in figure.
x^2 = 11^2 + 7^2 - 2×11×7×cos(90+θ)
x^2 = 121 + 49 + 154 × sinθ --------(1)
From triangle (2):
sinθ = 2/d
and by Pythagoras theorem
x^2 + 2^2 = d^2
Apply this in equation (1)
d^2 - 4 = 121 + 49 + 154 × 2/d
d^2 = 174 + 308/d -------(2)
As we know line joining any two points in a circle is always less than or equal to diameter
By this, d > 11
Now only way is to use trial method in equation (2)
By this we will get our solution.
d = 14
This puzzle can also solved by plotting center of circle and joining each point on that circle. Then apply cosine rule and consider sum of all angles at center is 180.
This is too lengthy method but you can get answer by some effort. I uploaded easiest method for this puzzle.
