Question

Prove $|AD|^2=|AB|\cdot |AC|-|DB|\cdot |DC|$ in triangle $ABC$, D the point where bisector of angle $A$ intersects $\overline {BC}$

score 145 · Answer 1 · 2018-09-06 19:51:51

Prove $|AD|^2=|AB|\cdot |AC|-|DB|\cdot |DC|$ in triangle $ABC$, D the point where bisector of angle $A$ intersects $\overline {BC}$

score 201 · Answer 2 · 2026-03-27 00:04:36

201

Views

Prove that $D$ is the incentre of the triangle $IJK$.

Published on 27 Mar 2026 - 0:04

score 101 · Answer 3 · 2026-03-27 08:39:02

101

Views

Basic similarity of triangles problem

Published on 27 Mar 2026 - 8:39

score 31 · Answer 4 · 2018-09-09 03:03:33

31

Views

Let $PAB'C, PBC'A, PCA'B$ form parallelograms so there exists a point $Q$.

Published on 09 Sep 2018 - 3:03

score 68 · Answer 5 · 2018-09-09 12:32:58

68

Views

$O$ is the orthocentre of $\triangle ABC$ if $AP\perp BC$, $BR\perp AC$ and $CQ \perp AB$. Prove that $\angle OPQ= \angle OPR$

Published on 09 Sep 2018 - 12:32

score 2k · Answer 6 · 2018-09-10 14:36:53

2k

Views

Covering the Euclidean plane with constructible lines and circles

Published on 10 Sep 2018 - 14:36

score 93 · Answer 7 · 2026-03-25 14:20:51

93

Views

Another beauty hidden in a simple triangle (3)

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score 108 · Answer 8 · 2026-03-27 15:35:40

108

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A convex quadrilateral with propotion

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score 121 · Answer 9 · 2026-03-25 15:41:20

121

Views

Compatibility of cross and inner product on $\mathbb{R}^3$

Published on 25 Mar 2026 - 15:41

score 1.1k · Answer 10 · 2026-03-25 01:26:17

1.1k

Views

How to algorithmically find only the edges of a high dimensional convex hull?

Published on 25 Mar 2026 - 1:26

score 71 · Answer 11 · 2026-03-30 12:25:43

71

Views

Geometric intepretation of matrix vector product

Published on 30 Mar 2026 - 12:25

score 680 · Answer 12 · 2018-09-12 03:00:52

680

Views

How to find the distance to pixel ratio in a image.

Published on 12 Sep 2018 - 3:00

score 171 · Answer 13 · 2026-03-25 11:12:23

171

Views

Inscribed square in circle generates three collinear points.

Published on 25 Mar 2026 - 11:12

score 409 · Answer 14 · 2026-03-25 17:17:19

409

Views

About Affine planes

Published on 25 Mar 2026 - 17:17

score 27 · Answer 15 · 2026-03-27 17:24:23

27

Views

Euclidean geometry as left invariant metric on Bianchi groups of type I or VII0

Published on 27 Mar 2026 - 17:24

List Question

Prove $|AD|^2=|AB|\cdot |AC|-|DB|\cdot |DC|$ in triangle $ABC$, D the point where bisector of angle $A$ intersects $\overline {BC}$

Prove that $D$ is the incentre of the triangle $IJK$.

Basic similarity of triangles problem

Let $PAB'C, PBC'A, PCA'B$ form parallelograms so there exists a point $Q$.

$O$ is the orthocentre of $\triangle ABC$ if $AP\perp BC$, $BR\perp AC$ and $CQ \perp AB$. Prove that $\angle OPQ= \angle OPR$

Covering the Euclidean plane with constructible lines and circles

Another beauty hidden in a simple triangle (3)

A convex quadrilateral with propotion

Compatibility of cross and inner product on $\mathbb{R}^3$

How to algorithmically find only the edges of a high dimensional convex hull?

Geometric intepretation of matrix vector product

How to find the distance to pixel ratio in a image.

Inscribed square in circle generates three collinear points.

About Affine planes

Euclidean geometry as left invariant metric on Bianchi groups of type I or VII0

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