Question

Proving the converse of Ceva's theorem

score 135 · Answer 1 · 2020-06-12 05:34:44

135

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Proving the converse of Ceva's theorem

Published on 12 Jun 2020 - 5:34

score 1.2k · Answer 2 · 2026-04-03 07:42:06

1.2k

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Radius of circle that touches 3 circles, which in turn touch each other

Published on 03 Apr 2026 - 7:42

score 42 · Answer 3 · 2026-03-25 16:02:02

42

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Problem on an isosceles right triangle, involving similarity and congruence

Published on 25 Mar 2026 - 16:02

score 51 · Answer 4 · 2026-03-28 13:41:52

51

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Prove that $d^2=a^2+b^2+c^2-2[ab\cos B+bc\cos C+ac\cos(α)]$

Published on 28 Mar 2026 - 13:41

score 439 · Answer 5 · 2026-04-01 09:37:52

439

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Given a random point and a cube, how can I determine the distance from that point to the furthest possible point on the cube?

Published on 01 Apr 2026 - 9:37

score 23 · Answer 6 · 2026-03-25 15:42:31

23

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If we have the slope of $AB$ and $AC$. How can we determine the angle of $AB$ and $AC$?

Published on 25 Mar 2026 - 15:42

score 115 · Answer 7 · 2026-02-25 15:39:41

115

Views

Billiards in an ellipse -- a query from a proof

Published on 25 Feb 2026 - 15:39

score 47 · Answer 8 · 2026-03-28 22:37:58

47

Views

A convex quadrilateral with sides $a$, $b$, $c$ has maximal area when its fourth side satisfies $x^3-(a^2+b^2+c^2)x-2abc=0$

Published on 28 Mar 2026 - 22:37

score 273 · Answer 9 · 2026-03-29 06:55:02

273

Views

A geometry problem to prove three line segments intersect at the same point

Published on 29 Mar 2026 - 6:55

score 30 · Answer 10 · 2026-04-11 12:25:14

30

Views

Defining a line from an inequality

Published on 11 Apr 2026 - 12:25

score 136 · Answer 11 · 2026-04-11 21:33:52

136

Views

An old APMO problem involving combinatorial geometry

Published on 11 Apr 2026 - 21:33

score 34 · Answer 12 · 2020-06-15 05:43:51

34

Views

Prove that distance between foot of perpendiculars from an arbitrary point on circle to two given diameters is constant.

Published on 15 Jun 2020 - 5:43

score 1k · Answer 13 · 2026-04-05 21:16:45

1k

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In triangle $ABC$, $\angle C = 48^\circ$. $D$ is any point on $BC$, such that $\angle CAD = 18^\circ$ and $AC = BD$. Find $\angle ABD.$

Published on 05 Apr 2026 - 21:16

score 500 · Answer 14 · 2026-04-03 15:46:29

500

Views

Show that the normal line of a parabola at point P...

Published on 03 Apr 2026 - 15:46

score 487 · Answer 15 · 2026-03-27 01:00:15

487

Views

Olympiad question: In the regular pentagon $ABCDE$, the perpendicular at $C$ to $CD$ meets $AB$ at $F$. Prove that $AE + AF = BE$.

Published on 27 Mar 2026 - 1:00

List Question

Proving the converse of Ceva's theorem

Radius of circle that touches 3 circles, which in turn touch each other

Problem on an isosceles right triangle, involving similarity and congruence

Prove that $d^2=a^2+b^2+c^2-2[ab\cos B+bc\cos C+ac\cos(α)]$

Given a random point and a cube, how can I determine the distance from that point to the furthest possible point on the cube?

If we have the slope of $AB$ and $AC$. How can we determine the angle of $AB$ and $AC$?

Billiards in an ellipse -- a query from a proof

A convex quadrilateral with sides $a$, $b$, $c$ has maximal area when its fourth side satisfies $x^3-(a^2+b^2+c^2)x-2abc=0$

A geometry problem to prove three line segments intersect at the same point

Defining a line from an inequality

An old APMO problem involving combinatorial geometry

Prove that distance between foot of perpendiculars from an arbitrary point on circle to two given diameters is constant.

In triangle $ABC$, $\angle C = 48^\circ$. $D$ is any point on $BC$, such that $\angle CAD = 18^\circ$ and $AC = BD$. Find $\angle ABD.$

Show that the normal line of a parabola at point P...

Olympiad question: In the regular pentagon $ABCDE$, the perpendicular at $C$ to $CD$ meets $AB$ at $F$. Prove that $AE + AF = BE$.

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