Question

In $\Delta ABC$, $D,E,F$ are points on the sides $BC,CA,AB$ respectively, such that the lines joining them are concurrent at a point $G$.

score 245 · Answer 1 · 2026-04-16 16:00:42

245

Views

In $\Delta ABC$, $D,E,F$ are points on the sides $BC,CA,AB$ respectively, such that the lines joining them are concurrent at a point $G$.

Published on 16 Apr 2026 - 16:00

score 602 · Answer 2 · 2026-04-17 07:21:26

602

Views

In $\Delta ABC$, bisector of $\angle A$ intersects $BC$ at $D$. A perpendicular from $B$ to $AD$ is drawn intersecting it at $E$.

Published on 17 Apr 2026 - 7:21

score 233 · Answer 3 · 2026-04-17 12:57:39

233

Views

2 identities of Shanks from Apostol's Book

Published on 17 Apr 2026 - 12:57

score 401 · Answer 4 · 2026-04-16 10:36:58

401

Views

If $AE$ and $BF$ are medians drawn to the legs of a right $\Delta ABC$, find the numerical value of $\frac{(AE)^2 + (BF)^2}{(AB)^2}$ .

Published on 16 Apr 2026 - 10:36

score 450 · Answer 5 · 2026-03-25 16:03:01

450

Views

In right $\Delta ABC$, $\angle C = 90^\circ$. $E$ is on $BC$ such that $AC = BE$. $D$ is on $AB$ such that $DE \perp BC$ .

Published on 25 Mar 2026 - 16:03

score 161 · Answer 6 · 2026-03-25 16:03:29

161

Views

In $\Delta ABC$, $AC = BC$ and $\angle C = 120^\circ$. $M$ is on side $AC$ and $N$ is on side $BC$ .

Published on 25 Mar 2026 - 16:03

score 374 · Answer 7 · 2026-03-25 17:39:23

374

Views

In $\Delta ABC$, angle bisector of $\angle ABC$ and median on side $BC$ intersect perpendicularly

Published on 25 Mar 2026 - 17:39

score 979 · Answer 8 · 2026-03-25 19:09:56

979

Views

When extending the sides $AB,BC,CA$ of $\Delta ABC$ to $B',C',A'$ respectively, such that $AB' = 2AB$ , $CC' = 2BC$ , $AA' = 3CA$ .

Published on 25 Mar 2026 - 19:09

score 890 · Answer 9 · 2026-04-15 05:33:53

Given a point $P$ outside equilateral $\Delta ABC$ but inside $\angle ABC$, if the distance between $P$ to $BC,CA,AB$ are $h_1,h_2,h_3$ respectively.

score 1k · Answer 10 · 2026-04-16 02:57:26

1k

Views

Given that $G$ is the centroid of $\Delta ABC$, $GA = 2\sqrt{3}$ , $GB = 2\sqrt{2}$, $GC = 2$ . Find $[\Delta ABC]$.

Published on 16 Apr 2026 - 2:57

score 90 · Answer 11 · 2026-04-12 12:20:39

90

Views

How to prove this is a probability density function?

Published on 12 Apr 2026 - 12:20

score 250 · Answer 12 · 2026-04-17 04:59:45

250

Views

How many different possible remainders of a square number modulo an odd prime?

Published on 17 Apr 2026 - 4:59

score 204 · Answer 13 · 2026-04-16 02:25:47

204

Views

A circle is centered at (2, 1) and tangent to the line x+y=0.

Published on 16 Apr 2026 - 2:25

score 149 · Answer 14 · 2026-04-13 22:17:01

149

Views

Falkner Skan solution using a tridiagonal matrix method. For 0, -ve $\beta$ I get incorrect solutions?

Published on 13 Apr 2026 - 22:17

score 222 · Answer 15 · 2026-04-13 11:39:48

222

Views

IMO 2020 question 6 about the proof of the correctness of a statement, involving planar geometry

Published on 13 Apr 2026 - 11:39

List Question

In $\Delta ABC$, $D,E,F$ are points on the sides $BC,CA,AB$ respectively, such that the lines joining them are concurrent at a point $G$.

In $\Delta ABC$, bisector of $\angle A$ intersects $BC$ at $D$. A perpendicular from $B$ to $AD$ is drawn intersecting it at $E$.

2 identities of Shanks from Apostol's Book

If $AE$ and $BF$ are medians drawn to the legs of a right $\Delta ABC$, find the numerical value of $\frac{(AE)^2 + (BF)^2}{(AB)^2}$ .

In right $\Delta ABC$, $\angle C = 90^\circ$. $E$ is on $BC$ such that $AC = BE$. $D$ is on $AB$ such that $DE \perp BC$ .

In $\Delta ABC$, $AC = BC$ and $\angle C = 120^\circ$. $M$ is on side $AC$ and $N$ is on side $BC$ .

In $\Delta ABC$, angle bisector of $\angle ABC$ and median on side $BC$ intersect perpendicularly

When extending the sides $AB,BC,CA$ of $\Delta ABC$ to $B',C',A'$ respectively, such that $AB' = 2AB$ , $CC' = 2BC$ , $AA' = 3CA$ .

Given a point $P$ outside equilateral $\Delta ABC$ but inside $\angle ABC$, if the distance between $P$ to $BC,CA,AB$ are $h_1,h_2,h_3$ respectively.

Given that $G$ is the centroid of $\Delta ABC$, $GA = 2\sqrt{3}$ , $GB = 2\sqrt{2}$, $GC = 2$ . Find $[\Delta ABC]$.

How to prove this is a probability density function?

How many different possible remainders of a square number modulo an odd prime?

A circle is centered at (2, 1) and tangent to the line x+y=0.

Falkner Skan solution using a tridiagonal matrix method. For 0, -ve $\beta$ I get incorrect solutions?

IMO 2020 question 6 about the proof of the correctness of a statement, involving planar geometry

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