Questions tagged [triangle]

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

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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
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
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
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
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
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
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
  • 23.4k