Question

Is a finite tiling of 45-45-90 triangles uniquely determined from the resulting union (up to trivial flips)?

score 228 · Answer 1 · 2026-04-15 08:33:35

228

Views

Is a finite tiling of 45-45-90 triangles uniquely determined from the resulting union (up to trivial flips)?

Published on 15 Apr 2026 - 8:33

score 66 · Answer 2 · 2026-04-15 05:05:33

66

Views

If $H$ is the orthocenter and $D,E,F$ are foot of altitudes prove that $\frac{AD}{HD}+\frac{BC}{HE}+\frac{CF}{HF}≥9$

Published on 15 Apr 2026 - 5:05

score 743 · Answer 3 · 2026-04-23 14:31:10

743

Views

A circle with diameter $AC$ is intersected by a secant at points $B,D$. The secant and the diameter intersect at point $P$ outside the circle.

Published on 23 Apr 2026 - 14:31

score 26 · Answer 4 · 2026-04-16 07:12:57

26

Views

Side lengths of a triangle satisfy $ab+bc+ca=3$. Prove that $3≤a+b+c≤2√3$

Published on 16 Apr 2026 - 7:12

score 129 · Answer 5 · 2026-04-12 18:44:17

129

Views

Three isosceles triangles △ABC', △AB'C, and △A'BC were constructed on the sides of triangle ABC.

Published on 12 Apr 2026 - 18:44

score 35 · Answer 6 · 2026-04-15 17:53:59

35

Views

Solving for point P within the edge AC, given points A, B and C, and length from B to P?

Published on 15 Apr 2026 - 17:53

score 1k · Answer 7 · 2026-04-16 07:10:50

1k

Views

How many pillars do we need to surround a triangular area?

Published on 16 Apr 2026 - 7:10

score 27 · Answer 8 · 2026-04-13 16:33:24

27

Views

How to find the B(x2, y2) poin on a chart knowing the angle, the segment length and point A(x1, y1)

Published on 13 Apr 2026 - 16:33

score 61 · Answer 9 · 2026-04-14 17:47:42

61

Views

How to calculate the number of side of a polygon?

Published on 14 Apr 2026 - 17:47

score 341 · Answer 10 · 2026-04-13 05:34:42

341

Views

Show that a triangle delimited by parallel lines to the sides of another triangle is similar to said triangle.

Published on 13 Apr 2026 - 5:34

score 272 · Answer 11 · 2026-04-23 19:22:57

272

Views

Let a circle with diameter $AB$ have points $C$ and $D$ on same side so that $BD$ bisects $\angle CBA$. Chords $AC$ and $BD$ intersect at $E$.

Published on 23 Apr 2026 - 19:22

score 227 · Answer 12 · 2026-04-30 14:50:27

227

Views

Prove that the sum of the radii of the circles

Published on 30 Apr 2026 - 14:50

score 55 · Answer 13 · 2026-04-11 03:18:54

55

Views

Geometry problem about area of triangle.

Published on 11 Apr 2026 - 3:18

score 192 · Answer 14 · 2026-04-09 17:13:29

192

Views

A hard geometry problem involving harmonic divisions

Published on 09 Apr 2026 - 17:13

score 103 · Answer 15 · 2026-04-09 17:15:28

103

Views

Properties of an apparently new triangle centre with trilinear coordinates $\frac1{\sqrt{a\cos A}}:\frac1{\sqrt{b\cos B}}:\frac1{\sqrt{c\cos C}}$

Published on 09 Apr 2026 - 17:15

List Question

Is a finite tiling of 45-45-90 triangles uniquely determined from the resulting union (up to trivial flips)?

If $H$ is the orthocenter and $D,E,F$ are foot of altitudes prove that $\frac{AD}{HD}+\frac{BC}{HE}+\frac{CF}{HF}≥9$

A circle with diameter $AC$ is intersected by a secant at points $B,D$. The secant and the diameter intersect at point $P$ outside the circle.

Side lengths of a triangle satisfy $ab+bc+ca=3$. Prove that $3≤a+b+c≤2√3$

Three isosceles triangles △ABC', △AB'C, and △A'BC were constructed on the sides of triangle ABC.

Solving for point P within the edge AC, given points A, B and C, and length from B to P?

How many pillars do we need to surround a triangular area?

How to find the B(x2, y2) poin on a chart knowing the angle, the segment length and point A(x1, y1)

How to calculate the number of side of a polygon?

Show that a triangle delimited by parallel lines to the sides of another triangle is similar to said triangle.

Let a circle with diameter $AB$ have points $C$ and $D$ on same side so that $BD$ bisects $\angle CBA$. Chords $AC$ and $BD$ intersect at $E$.

Prove that the sum of the radii of the circles

Geometry problem about area of triangle.

A hard geometry problem involving harmonic divisions

Properties of an apparently new triangle centre with trilinear coordinates $\frac1{\sqrt{a\cos A}}:\frac1{\sqrt{b\cos B}}:\frac1{\sqrt{c\cos C}}$

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