# Questions tagged [triangle]

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

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### 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 ...
• 1,601
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 ...
• 383
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 ...
• 351
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?
• 338
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 ...
• 3,978
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, ...
• 45.6k
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### 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 ...
• 21.6k
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. ...
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 ...
• 23.5k
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. ...
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### 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 ...
• 45.6k
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 ...
• 4,133
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 ...
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 ...
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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.
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 ...
• 1,056
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 ...
• 3,978
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 ...
• 3,978
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 ...
• 7,845
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 ...
• 3,614
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 ...
• 9,886
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 ...
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?
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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 ...
• 3,978
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
• 131
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 ...
• 621
1 vote
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 ...
• 111
1 vote
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) ...
• 2,239
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?
• 13
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?
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 ...
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 ...
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