A larger one
Find the total number of triangles(excluding degenerate triangles) and quadrilaterals in the given figure.
Details
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G,H lie on EF. P,O lie on KL.
Line segment EGHF is parallel to AB.
C is a point on the other side of AB compared to EGHF.
There are 41 additional points on the line segment GH, which are connected to both A and B with line segments.
There are 41 additional points on the line segment HF, which are connected to B with line segments.
There are 41 additional points on the line segment GE, which are connected to A with line segments.
There are 27 additional points on the line segment GC, which are connected to B with line segments.
There are 27 additional points on the line segment BC, which are connected to A with line segments.
JI and MN are parallel KO and are on opposite sides of KO.
PO is extended to K on the left and L on the right.
J and K, K and M, L and N, I and L, are connected together with curves (which is one-fourth the circumference of the circle drawn with radius KP and OL respectively).
There are 15 additional points on each arc JK, KM, LN and IL and they are connected to both P and O by line segments.
Hint : J K , K M , I L and L N are a r c s so there are no I n d i v i d u a l T r i a n g l e s in it.
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1 solution
Anyone, like my question?
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Yes sir!!!
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Sir?? I am younger than you. 1 5 years old
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@Ashish Menon – so what, you are much better than me :-) :-)
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@Atul Shivam – Thank y o u . But I think you are better
Try "Plenty of Dots", "Taking it to the next level", "OMG!". "OMG! 2 " and "Another nice question".
The s o u r c e of the question is my b r a i n
Very lengthy problem but nice :-) :-)
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Thank you B H A I Y Y A . Did u solve the same way I did?
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yes!!! almost same way, BTW I have gone through most of ur problems they are great
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@Atul Shivam – Thank you did you see "Triangles again" . No one has been able to solve it as yet. I hope you would be able to do it.
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@Ashish Menon – Oh really? I think I told you that I have solved it. Want a proof I can send you a screenshot.( just joking, btw I really solved it) anyways yet another truly awesome problem posted by you.
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@Rishabh Sood – What? But it is shown that no one has solved it as yet. The question is T R I A N G L E S A G A I N
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@Ashish Menon – I know, somethings wrong with brilliant. You know what, someone fumbled with problems I posted. The figure changes on its own and the title of the question changed too.
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@Rishabh Sood – Just tell me one thing, how do you draw such complicated figures?
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@Rishabh Sood – I started, with 5 triangles in the same base.then I went for 10 quadrilaterals in the same base. I modified it more and more and more and I arrived at my digure
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@Ashish Menon – Cool digures made by u, but I like the figure u make
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@Rishabh Sood – Thank y o u bro
@Rishabh Sood – Did u draw figures? I would try it right away
@Rishabh Sood – Do u like the following equation.
A S H I S H + R I S H A B H = B R O T H E R S F O R E V E R
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@Ashish Menon – no, erase friends and make it best brothers forever. just joking nice one and a correction I am "Rishabh" with a h
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@Rishabh Sood – okokok , next time
@Rishabh Sood – Did it. I edited the e q u a t i o n . Try my latest question C a l c u l a t o r ′ s w o r s t e n e m y .
@Rishabh Sood – Yes,it happened with me too. My question Triangles in a crown, was not the name I set for it. The picture which I had posted were hand - drawn. But now it is changed, but same pic
@Rishabh Sood – Thank you for telling that it is good
@Rishabh Sood – Of all my juniors, I think you are really outstanding in maths. A little more thinking and you can post figures as I do. Who knows, one day, you might be the best among all the brilliant members.
Total number of t r i a n g l e s = 2 ( 2 4 6 8 5 ) + 1 7 6 ( 4 2 + 4 1 + 4 0 + 3 9 + 3 8 + 3 7 + 3 6 + 3 5 + 3 4 + 3 3 + 3 2 + 3 1 + 3 0 + 2 9 + 2 8 + 2 7 + 2 6 + 2 5 + 2 4 + 2 3 + 2 2 + 2 1 + 2 0 + 1 9 + 1 8 + 1 7 + 1 6 + 1 5 + 1 4 + 1 3 + 1 2 + 1 1 + 1 0 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 ) + 1 1 2 8 6 + 2 ( 1 3 1 4 4 9 ) + 2 ( 3 1 ) + 4
= 4 9 3 7 0 + 1 7 6 ( 9 0 3 ) + 1 1 2 8 6 + 2 6 2 8 9 8 + 6 2 + 4
= 4 9 3 7 0 + 1 5 8 9 2 8 + 1 1 2 8 6 + 2 6 2 8 9 8 + 6 2 + 4
= 4 8 2 5 4 8
Total number of q u a d r i l a t e r a l s = 2 ( 7 2 2 5 ) + 1 0 9 9 5 1 1 4 7 7 6 0 0 1 5 0 + 2 ( 3 4 5 9 ) + 7 2 4 4 1 6 + 8 5 3 7 7 6 + 1 1 + 5 7 4 4 9 6 + 2 9 0 3 6 1 6
= 1 4 4 5 0 1 0 9 9 5 1 1 4 7 7 6 0 0 1 5 0 + 6 9 1 8 + 7 2 4 4 1 6 + 8 5 3 7 7 6 + 1 1 + 5 7 4 4 9 6 + 2 9 0 3 6 1 6
= 1 0 9 9 5 1 1 4 8 2 6 7 7 7 7 1
Therefore, total number of t r i a n g l e s and q u a d r i l a t e r a l s = 1 0 9 9 5 1 1 4 8 2 6 7 7 7 7 1 + 4 8 2 5 4 8
= 1 0 9 9 5 1 1 4 8 3 1 6 0 3 1 9