Questions tagged [triangle]

A geometry puzzle centered around the triangle or the centers of a triangle.

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33 votes
5 answers
2k views

Slicing a rectangle

A friend presented this nice little puzzle to me yesterday. You're given a rectangle which is dissected by one of its diagonals, as well as another line that only meets one of the two remaining ...
Martin Ender's user avatar
  • 1,601
27 votes
4 answers
4k views

What is the most triangles you can make from a capital "H" and 3 straight lines?

So start with an upper case H, and then draw $3$ straight lines. What is the greatest number of closed triangles that you can form? For example: Note that triangles inside of triangles only count ...
Curtis's user avatar
  • 383
20 votes
7 answers
2k views

Triangle in a circle

Suppose three points are chosen at random in a circle. A triangle is made with these three points as vertices. What's the probability that the triangle contains the origin of the circle? (Although I ...
Simon S's user avatar
  • 351
12 votes
2 answers
1k views

Prove why this mechanical linkage for a triangle centroid works

I saw on Twitter this cool mechanical linkage for which the red dot corresponds to the centroid of the triangle defined by the blue dots: Can you prove why this linkage works?
Kikos's user avatar
  • 338
11 votes
2 answers
717 views

Unlucky tiling: Arrange thirteen right isosceles triangles into a square

Link to next puzzle in this series:Five graded difficulty isosceles right triangle into square tilings Two difficult "Seventeen right isosceles triangles into a square" tilings V.hard ...
theonetruepath's user avatar
10 votes
3 answers
846 views

The Erasmus isosceles triangle

Professor Erasmus has constructed a special isosceles triangle that he modestly calls the "Professor-Erasmus-triangle". The professor claims that he can cut his triangle into three smaller triangles, ...
Gamow's user avatar
  • 45.6k
9 votes
2 answers
1k views

3D? No-no! 3 Sides

Introducing the Isometric Nonogram! α) "Boar"ing Definition [oink] Column: Blue Part + Green Cell Row: Yellow Part + Green Cell Adjacent/ Continuous cells: Purple Cell + any of the Orange ...
Omega Krypton's user avatar
9 votes
3 answers
477 views

Special triangles in convex polygons

Given identical 30-60-90 triangles, what is the convex polygon with the highest number of sides that I can build from them? This seems a very easy task by first look, but I’m totally stuck right now. ...
Francesco Arnaudo's user avatar
8 votes
3 answers
464 views

A circle touches two sides of a triangle and two of its medians

A circle touches two sides of a triangle and two of its medians. Prove that the triangle is isosceles. This problem came from the Mathematical Digest issue 62 (Jan 1986) which in turn cited a Russian ...
Dr Xorile's user avatar
  • 23.5k
8 votes
2 answers
575 views

Triangles to diamonds

Given a triangle ABC with sides a=|BC|,b=|CA|,c=|AB| a diamond is circumscribed around the triangle's incircle. The diamond and the triangle share the corner C along with (part of) sides a and b. ...
Albert.Lang's user avatar
  • 5,237
8 votes
1 answer
329 views

The Erasmus tedrahedron

Professor Erasmus has constructed a special tetrahedron that he modestly calls the "Professor-Erasmus-tetrahedron". The professor claims that all four faces of his tedrahedron are right-angled and ...
Gamow's user avatar
  • 45.6k
7 votes
3 answers
2k views

Can you make 10 triangles with just 10 sticks?

Can you make 10 triangles with just 10 sticks? The sticks don't have to have the same length. Hint 1: Hint 2: There are several other possibilities than the one I gave hints for. I recently found ...
wythagoras's user avatar
  • 4,133
7 votes
1 answer
352 views

What percentage of blue? [closed]

Lines are drawn parallel to the base of the triangle, dividing the other sides into 10 equal parts. Every second strip is painted blue. Question What is the percentage of blue color in the ...
user avatar
6 votes
2 answers
384 views

Independent Triangles with Straight Lines

Your task is to create independent triangles (which means they do not have the same edge) by drawing straight lines as exemplified below: In this example, there are $5$ lines and $5$ independent ...
Oray's user avatar
  • 30.3k
5 votes
1 answer
283 views

Circle inscribed in triangle problem [closed]

You need to find the angle BEC knowing that the side BC is tangent to the circumference.
user78580's user avatar
5 votes
1 answer
186 views

Find the least expense?

You want to build a shop between three roads in the shape of an equilateral triangle. What would be the best location for the shop so that you can reach each road with the minimum transportation ...
Sayed Mohd Ali's user avatar
5 votes
2 answers
275 views

Five graded difficulty isosceles right triangle into square tilings

Similar to: Unlucky tiling: Arrange thirteen right isosceles triangles into a square Two difficult "Seventeen right isosceles triangles into a square" tilings V.hard problem, 20 right ...
theonetruepath's user avatar
5 votes
2 answers
507 views

20 right isosceles triangles into a square

Similar: Unlucky tiling: Arrange thirteen right isosceles triangles into a square Five graded difficulty isosceles right triangle into square tilings Two difficult "Seventeen right isosceles ...
theonetruepath's user avatar
4 votes
2 answers
691 views

A geometric puzzle. What is the angle?

This is a simply stated geometry puzzle. What is the angle p in this isosceles triangle? Here's some information about the origin of the puzzle. Following any links therein may spoil the fun if you ...
Simd's user avatar
  • 7,845
4 votes
0 answers
229 views

2018 January Challenge: Geometry [closed]

Considering it's the beginning of a new year, I have created the following challenge. I hope to make one every month until December 2018! Here goes: Show that $AD-AB>AC^3$. Do not use scale ...
ə̷̶̸͇̘̜́̍͗̂̄︣͟'s user avatar
3 votes
5 answers
1k views

Professor Rackbrane: Count the triangles

Professor Rackbrane has just given me the following puzzle as an example of those that interested his party at Christmas. Draw a pentagon, and connect each point with every other point by straight ...
Will Octagon Gibson's user avatar
3 votes
6 answers
1k views

Find the total number of triangles in the diagram

The title of the question says everything $\ldots$ My attempt: We count $2(1+1+1+2+1+1+2+1+1+1+1)=26$ triangles. (On each side $13$ triangles, and then multiplied by $2$). And then we combine them ...
Aditya Agarwal's user avatar
3 votes
2 answers
207 views

A triangle inside a triangle

All sides of a triangle T1 are shorter than the shortest side of a triangle T2. Is it always possible to put triangle T1 completely inside triangle T2?
ThomasL's user avatar
  • 12.2k
2 votes
2 answers
208 views

Two difficult "Seventeen right isosceles triangles into a square" tilings

Similar to: Unlucky tiling: Arrange thirteen right isosceles triangles into a square Five graded difficulty isosceles right triangle into square tilings V.hard problem, 20 right isosceles triangles ...
theonetruepath's user avatar
2 votes
1 answer
221 views

How to map barycentric indices to a single integer? [closed]

how can one map barycentric indices to a single integer? e.g. Edit: added correct image
Joe's user avatar
  • 131
2 votes
0 answers
137 views

Multiple Line Lengths around 8 triangles

The image below contains 8 triangles each having side length 6. Inside each triangles are three numbers indicating lengths of 3 lines that are wrapped around the triangle without gaps. Numbers range ...
Maff's user avatar
  • 621
1 vote
1 answer
102 views

Can you help me out with this question? [closed]

I found that 3abc+a+b+c formula is correct first and second triangle. But the result for third triangle isn't in the options. Can you find another solution? Source: It's from an old job admission ...
frkntrn's user avatar
  • 111
1 vote
1 answer
943 views

Four similar triangles

The challenge as described hereafter is to create a total of 4 similar triangles by drawing 4 triangle in a scalene, acute triangle - out of the 5 resulting triangles (4 that make the original one) ...
Moti's user avatar
  • 2,239
0 votes
1 answer
472 views

Triangle partial length of hypotenuse [closed]

How can I solve for X? What I did was solve for C, and then took (6/6+2)*C. It seems to work but I am not completely sure. Is there a better way?
amikic's user avatar
  • 13
-1 votes
2 answers
136 views

Surrounding an equilateral triangle

You are given an equilateral triangle. What is the most number of such identical triangles you can place such that they do not overlap, but each one touches the original triangle?
Dmitry Kamenetsky's user avatar
-1 votes
2 answers
570 views

That's a lot of triangles

Counting the Triangles in this image individually would take far too long. Can anyone come up with an algorithm to figure out how many triangles are in this shape? Answers should include the number ...
Chase Sandmann's user avatar
-1 votes
1 answer
233 views

Trianglify the Shapes

For each of the following shapes, draw extra lines to divide the shape into the smallest number of triangles that can completely fill the shape. Example: Solution: Shapes (a correct answer answers ...
john01dav's user avatar
  • 297
-4 votes
1 answer
146 views

How many cubes is this tringle made of? [closed]

can you guess? i know its a simple puzzle but lest just have fun
Navid2132's user avatar
  • 455
-4 votes
1 answer
136 views

Can you help to solve this triangle puzzle [closed]

Find the missing number (triangle) Please write the logic also.
DARDAR SAAD's user avatar