Consider this diagram. Half of the line segments are drawn in red. The line segments $a_0b_1,b_1a_2,a_2b_3,b_3a_4$ also exist, but are ommited here for clarity. We do not yet know what angle $x$ is, but we can work out the other angles in terms of $x$. We will be working in radians here. $\pi\ radians = 180\ degrees$ Because the slice is an isosceles triangle, we can calculate: $c = \frac{\pix}{2} = 0.5\pi  0.5x$ Knowing that all the inner triangles are also isosceles trangles, we can also calculate: $d = \pi  2c = x$ $e = c  d = 0.5\pi  1.5x$ $f = \pi  2e = 3x$ $g = \pi  c  f = 0.5\pi 2.5x$ $h = \pi  2g = 5x$ $i = \pi  e  h = 0.5\pi  3.5x$ $j = \pi  2i = 7x$ Also because of the isosceles triangle, $x = i$, so we can now derive the value of $x$: $x = 0.5\pi  3.5x$ $4.5x = 0.5\pi$ $9x = \pi$ Now we can go back and substitute $\frac{\pi}{9}$ for $x$ and work out all the angles exactly. We can also see a pattern in the angles. The angles of the tops of the triangles go: $x,3x,5x,7x..$ while the angles of the sides go $0.5\pi0.5x$ $0.5\pi1.5x$ $0.5\pi2.5x$ $0.5\pi3.5x$ $..$ So we can work out the angles of specific triangles with closed form formula, instead of having to calculate them all. asked 14 Jan, 18:00

Answer is hidden as author is suspended. Click here to view.
answered 14 Jan, 19:40

I really appreciate this editorial, more clear thought process. I agree to karan that it's better than original. answered 14 Jan, 20:31

Since a0a1b2 is isosceles as side a0a1 = a1b2 so i = x, but you are saying i = 0.5π  3.5x, so i think it is wrong answered 14 Jan, 23:40

Plagiarism: XYPIZQ https://www.codechef.com/viewsolution/22482771 https://www.codechef.com/viewsolution/22482425 https://www.codechef.com/viewsolution/22483248 https://www.codechef.com/viewsolution/22482660 answered 15 Jan, 13:55
