In a given straight line AB, find a point P such that the difference in the squares on AP and PB is equal to the difference between two given squares.

score 260 · Answer 7 · 2026-03-27 18:48:38

260

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Find the value of $\angle BDE$

Published on 27 Mar 2026 - 18:48

score 134 · Answer 8 · 2026-02-23 02:50:11

134

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Let $a,b,c$ be side lengths of a triangle, $a+b+c=1$. Prove that $P=a^3+b^3+c^3+3abc<\frac{1}{4}$.

Published on 23 Feb 2026 - 2:50

score 61 · Answer 9 · 2026-04-03 02:57:46

61

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Given $\cos C(\sin A +\sin B)=\sin C \cos(A-B)$, prove that triangle $ABC$ is equilateral.

Published on 03 Apr 2026 - 2:57

score 3.1k · Answer 10 · 2020-04-11 18:13:37

3.1k

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Langley's Adventitious Angles${}$

Published on 11 Apr 2020 - 18:13

score 189 · Answer 11 · 2020-04-11 20:05:00

189

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Find the area of the triangle $\triangle ABC$ embedded in a circle

Published on 11 Apr 2020 - 20:05

score 473 · Answer 12 · 2026-03-27 20:31:40

473

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Solve for the angle UFO with the russian triangle

Published on 27 Mar 2026 - 20:31

score 252 · Answer 13 · 2026-03-26 06:30:10

252

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Are there geodesic triangles on surfaces with non-constant curvature with angle sum 180?

Published on 26 Mar 2026 - 6:30

score 1.4k · Answer 14 · 2020-04-13 10:48:03

1.4k

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Prove that external bisectors of the angles of a triangle meet the opposite sides in three collinear points.

Published on 13 Apr 2020 - 10:48

score 388 · Answer 15 · 2020-04-13 11:54:25

388

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Prove that the sides of the orthic triangle meet the sides of the given triangle in three collinear points.

Published on 13 Apr 2020 - 11:54

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In a given straight line AB, find a point P such that the difference in the squares on AP and PB is equal to the difference between two given squares.

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Let $a,b,c$ be side lengths of a triangle, $a+b+c=1$. Prove that $P=a^3+b^3+c^3+3abc<\frac{1}{4}$.

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