Question

Show $\triangle AES$ is equilateral iff $\triangle IKE$ is equilateral....

score 153 · Answer 1 · 2023-10-03 11:31:24

153

Views

Show $\triangle AES$ is equilateral iff $\triangle IKE$ is equilateral....

Published on 03 Oct 2023 - 11:31

score 114 · Answer 2 · 2026-04-08 17:55:25

114

Views

How to find angle $x$?

Published on 08 Apr 2026 - 17:55

score 221 · Answer 3 · 2023-10-04 04:20:20

221

Views

Point $D$ in $\triangle{ABC}$ such that $\angle{DBC}=\angle{DCB}=10^{\circ}$, $\angle{BAD}=20^{\circ}, \angle{DAC}=40^{\circ}$, show that $AD=AC$

Published on 04 Oct 2023 - 4:20

score 60 · Answer 4 · 2026-04-11 05:10:15

60

Views

Proving that angle measurement is well defined

Published on 11 Apr 2026 - 5:10

score 84 · Answer 5 · 2023-10-04 15:50:46

84

Views

Prove that: $a^3\cos{B}\cos{C} + b^3\cos{C}\cos{A} + c^3\cos{A}\cos{B} = abc(1-2\cos{A}\cos{B}\cos{C}).$

Published on 04 Oct 2023 - 15:50

score 46 · Answer 6 · 2026-03-31 14:15:38

46

Views

Prove that $\sum_{cyc}{\tan^{-1}(\cot{B}\cot{C})}= \tan^{-1}{\left(1+\frac{8\cos{A}\cos{B}\cos{C}}{\sin^{2}{2A} +\sin^{2}{2B} + \sin^{2}{2C}}\right)}$

Published on 31 Mar 2026 - 14:15

score 153 · Answer 7 · 2026-03-29 08:14:46

153

Views

Show that triangle $ABC$ is equilateral

Published on 29 Mar 2026 - 8:14

score 177 · Answer 8 · 2023-10-05 17:11:35

177

Views

geometry problem involving a half equilateral triangle and its angle bissector - can it be solved without coordinate geometry?

Published on 05 Oct 2023 - 17:11

score 51 · Answer 9 · 2026-03-29 10:15:19

51

Views

Solving an Irregular Quadrilateral defined by a Circle intersecting with 2 Concentric Circles: their 2 Centers & the 2 Intersection Points

Published on 29 Mar 2026 - 10:15

score 49 · Answer 10 · 2026-03-25 07:45:52

49

Views

How to prove $EN=\dfrac{AI}{2}?$ and $KN=\dfrac{CJ}{2}$? and $\dfrac{Area(ABD)}{2}+\dfrac{Area(BCD)}{2}=\dfrac{Area(ABCD)}{2}$?

Published on 25 Mar 2026 - 7:45

score 167 · Answer 11 · 2023-10-09 11:49:27

167

Views

Three randomly placed points inside a unit circle. Probability that the formed triangle contains the centre of the circle inside?

Published on 09 Oct 2023 - 11:49

score 80 · Answer 12 · 2023-10-12 21:52:03

80

Views

How many "outward" triangles are needed on a circle so that when one is removed, each triangle consistently overlaps with two triangles on the circle?

Published on 12 Oct 2023 - 21:52

score 65 · Answer 13 · 2026-04-10 17:12:06

65

Views

Tangential tetrahedron

Published on 10 Apr 2026 - 17:12

score 28 · Answer 14 · 2023-10-13 19:06:06

28

Views

Is the derivation of the ratio R a Corollary to the Angle Bisector Theorem?

Published on 13 Oct 2023 - 19:06

score 173 · Answer 15 · 2023-10-13 20:14:05

173

Views

Find nature of triangle knowing that $a^3+b^3+c^3=3abc$

Published on 13 Oct 2023 - 20:14

List Question

Show $\triangle AES$ is equilateral iff $\triangle IKE$ is equilateral....

How to find angle $x$?

Point $D$ in $\triangle{ABC}$ such that $\angle{DBC}=\angle{DCB}=10^{\circ}$, $\angle{BAD}=20^{\circ}, \angle{DAC}=40^{\circ}$, show that $AD=AC$

Proving that angle measurement is well defined

Prove that: $a^3\cos{B}\cos{C} + b^3\cos{C}\cos{A} + c^3\cos{A}\cos{B} = abc(1-2\cos{A}\cos{B}\cos{C}).$

Prove that $\sum_{cyc}{\tan^{-1}(\cot{B}\cot{C})}= \tan^{-1}{\left(1+\frac{8\cos{A}\cos{B}\cos{C}}{\sin^{2}{2A} +\sin^{2}{2B} + \sin^{2}{2C}}\right)}$

Show that triangle $ABC$ is equilateral

geometry problem involving a half equilateral triangle and its angle bissector - can it be solved without coordinate geometry?

Solving an Irregular Quadrilateral defined by a Circle intersecting with 2 Concentric Circles: their 2 Centers & the 2 Intersection Points

How to prove $EN=\dfrac{AI}{2}?$ and $KN=\dfrac{CJ}{2}$? and $\dfrac{Area(ABD)}{2}+\dfrac{Area(BCD)}{2}=\dfrac{Area(ABCD)}{2}$?

Three randomly placed points inside a unit circle. Probability that the formed triangle contains the centre of the circle inside?

How many "outward" triangles are needed on a circle so that when one is removed, each triangle consistently overlaps with two triangles on the circle?

Tangential tetrahedron

Is the derivation of the ratio R a Corollary to the Angle Bisector Theorem?

Find nature of triangle knowing that $a^3+b^3+c^3=3abc$

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