Question

Equilateral triangle $ABC$ with $D$ on $BC$ such that $BD=\frac13BC$. Prove $9\overline{AD}^2=7\overline{AB}^2$

score 68 · Answer 1 · 2026-04-14 16:44:57

68

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Equilateral triangle $ABC$ with $D$ on $BC$ such that $BD=\frac13BC$. Prove $9\overline{AD}^2=7\overline{AB}^2$

Published on 14 Apr 2026 - 16:44

score 203 · Answer 2 · 2026-04-14 19:57:38

203

Views

Verifying the hyperbolic law of cosines and law of sines..

Published on 14 Apr 2026 - 19:57

score 584 · Answer 3 · 2026-04-13 11:47:03

584

Views

Closest point on ray to triangle in 3D

Published on 13 Apr 2026 - 11:47

score 450 · Answer 4 · 2026-04-12 01:26:10

450

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Maximum of the ratio of the incircle radius to the circumcircle radius for an arbitrary triangle

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score 146 · Answer 5 · 2026-04-09 17:13:10

146

Views

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score 170 · Answer 6 · 2026-04-11 14:09:13

170

Views

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score 234 · Answer 7 · 2026-04-15 08:25:19

234

Views

Find the length of AB in the given question.

Published on 15 Apr 2026 - 8:25

score 94 · Answer 8 · 2026-04-09 17:15:37

94

Views

Circumcircle of mid points of a triangle touching the circumcircle of the triangle

Published on 09 Apr 2026 - 17:15

score 208 · Answer 9 · 2026-04-19 16:07:11

208

Views

Geometrical combinatorics with $(n+1)^2$ points inside a square that determine a triangle

Published on 19 Apr 2026 - 16:07

score 179 · Answer 10 · 2026-04-16 12:09:38

179

Views

Area of triangle with incircle tangent to semicircle whose diameter is on one triangle side

Published on 16 Apr 2026 - 12:09

score 42 · Answer 11 · 2026-04-09 10:58:19

42

Views

Finding the height of a triangle without using trigonometry functions

Published on 09 Apr 2026 - 10:58

score 75 · Answer 12 · 2026-04-24 04:36:37

75

Views

Given an acute triangle in a circle, prove the concyclicity of some points

Published on 24 Apr 2026 - 4:36

score 532 · Answer 13 · 2026-04-14 11:54:14

532

Views

The hypotenuse of a triangle is shortest when the other two legs are equal. Prove this using the Calculus of Variations.

Published on 14 Apr 2026 - 11:54

score 252 · Answer 14 · 2026-05-05 11:49:41

252

Views

Is there a $\triangle ABC$, with $D$ on $BC$, such that $AB$, $BC$, $CA$, $AD$, $BD$, $CD$ are all integers, but only one is even?

Published on 05 May 2026 - 11:49

score 238 · Answer 15 · 2026-04-15 23:22:48

238

Views

Find angle $x$ in the isosceles $\triangle ABC$.

Published on 15 Apr 2026 - 23:22

List Question

Equilateral triangle $ABC$ with $D$ on $BC$ such that $BD=\frac13BC$. Prove $9\overline{AD}^2=7\overline{AB}^2$

Verifying the hyperbolic law of cosines and law of sines..

Closest point on ray to triangle in 3D

Maximum of the ratio of the incircle radius to the circumcircle radius for an arbitrary triangle

Geometry problem - prove that incentre of two triangles coincide

Nice geometry question to prove tangency

Find the length of AB in the given question.

Circumcircle of mid points of a triangle touching the circumcircle of the triangle

Geometrical combinatorics with $(n+1)^2$ points inside a square that determine a triangle

Area of triangle with incircle tangent to semicircle whose diameter is on one triangle side

Finding the height of a triangle without using trigonometry functions

Given an acute triangle in a circle, prove the concyclicity of some points

The hypotenuse of a triangle is shortest when the other two legs are equal. Prove this using the Calculus of Variations.

Is there a $\triangle ABC$, with $D$ on $BC$, such that $AB$, $BC$, $CA$, $AD$, $BD$, $CD$ are all integers, but only one is even?

Find angle $x$ in the isosceles $\triangle ABC$.

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