Question

In $\triangle ABC$, $AD$ $\perp$ $BC$ and $GE$ is the extended line of $DG$ where $G$ is centroid. Prove that $GD$ = $\frac{EG}{2}$

score 272 · Answer 1 · 2026-03-23 09:21:54

272

Views

In $\triangle ABC$, $AD$ $\perp$ $BC$ and $GE$ is the extended line of $DG$ where $G$ is centroid. Prove that $GD$ = $\frac{EG}{2}$

Published on 23 Mar 2026 - 9:21

score 121 · Answer 2 · 2026-03-28 09:28:40

121

Views

What is the area of $ABCD$ parallelogram where $E$ is mid-point of BC and the area of $BEC$ is 126?

Published on 28 Mar 2026 - 9:28

score 710 · Answer 3 · 2026-03-25 07:46:08

710

Views

We have $n$ charged and $n$ uncharged batteries and a radio which needs two charged batteries to work.

Published on 25 Mar 2026 - 7:46

score 879 · Answer 4 · 2019-02-16 14:08:45

Find a 10 digit number that contains all digits from 0 to 9 once, starts with a 3, and is also divisible by all whole numbers from 2 to 18

score 127 · Answer 5 · 2019-02-16 14:58:13

127

Views

What is the value of $a+b$ where the area of the square in the diagram is $\dfrac{a}{b}$ and both are co-primes?

Published on 16 Feb 2019 - 14:58

score 26 · Answer 6 · 2019-02-16 19:59:19

26

Views

Draw and study the discontinuous of $g(x)=\lfloor \sin(x) \rfloor$

Published on 16 Feb 2019 - 19:59

score 369 · Answer 7 · 2026-03-25 11:04:45

369

Views

Prove that inequality $\sqrt{2\sqrt{4\sqrt{8....\sqrt{2^n}}}} \leqslant n+1$

Published on 25 Mar 2026 - 11:04

score 135 · Answer 8 · 2019-02-17 05:43:38

135

Views

Evaluate this question based on series and limits.

Published on 17 Feb 2019 - 5:43

score 155 · Answer 9 · 2019-02-17 07:26:28

155

Views

Prove that $(a+b) (a^2 + b^2) (a^4 + b^4)...(a^{32} + b^{32}) = a^{64} - b^{64}$ if $b = a-1$

Published on 17 Feb 2019 - 7:26

score 528 · Answer 10 · 2026-03-26 13:07:29

528

Views

What is the probability if we throw dart towards a large square but it should hit only the inner part of small square $FEHG$ inscribed in it?

Published on 26 Mar 2026 - 13:07

score 76 · Answer 11 · 2026-03-27 05:38:12

76

Views

Compute: $\frac3{7\cdot2}+\frac3{7\cdot12}+\dots$

Published on 27 Mar 2026 - 5:38

score 283 · Answer 12 · 2026-03-26 16:26:41

283

Views

Understanding a proof from the APMO 1998 on inequalities.

Published on 26 Mar 2026 - 16:26

score 202 · Answer 13 · 2019-02-18 03:50:00

202

Views

Determinants Quadratic polynomials and iota in characteristic equation .

Published on 18 Feb 2019 - 3:50

score 787 · Answer 14 · 2026-03-25 07:46:00

787

Views

If $a$, $b$ and $c$ are sides of a triangle, then prove that $a^\text{2}(b+c-a) + b^\text{2}(c+a-b) + c^\text{2}(a+b-c)$ $\leqslant$ $3abc$

Published on 25 Mar 2026 - 7:46

score 112 · Answer 15 · 2019-02-18 23:48:32

112

Views

Solving $(x^2+4x+3)^x+(2x+4)^x=(x^2+4x+5)^x$ with $x\in(-1,\infty)$

Published on 18 Feb 2019 - 23:48

List Question

In $\triangle ABC$, $AD$ $\perp$ $BC$ and $GE$ is the extended line of $DG$ where $G$ is centroid. Prove that $GD$ = $\frac{EG}{2}$

What is the area of $ABCD$ parallelogram where $E$ is mid-point of BC and the area of $BEC$ is 126?

We have $n$ charged and $n$ uncharged batteries and a radio which needs two charged batteries to work.

Find a 10 digit number that contains all digits from 0 to 9 once, starts with a 3, and is also divisible by all whole numbers from 2 to 18

What is the value of $a+b$ where the area of the square in the diagram is $\dfrac{a}{b}$ and both are co-primes?

Draw and study the discontinuous of $g(x)=\lfloor \sin(x) \rfloor$

Prove that inequality $\sqrt{2\sqrt{4\sqrt{8....\sqrt{2^n}}}} \leqslant n+1$

Evaluate this question based on series and limits.

Prove that $(a+b) (a^2 + b^2) (a^4 + b^4)...(a^{32} + b^{32}) = a^{64} - b^{64}$ if $b = a-1$

What is the probability if we throw dart towards a large square but it should hit only the inner part of small square $FEHG$ inscribed in it?

Compute: $\frac3{7\cdot2}+\frac3{7\cdot12}+\dots$

Understanding a proof from the APMO 1998 on inequalities.

Determinants Quadratic polynomials and iota in characteristic equation .

If $a$, $b$ and $c$ are sides of a triangle, then prove that $a^\text{2}(b+c-a) + b^\text{2}(c+a-b) + c^\text{2}(a+b-c)$ $\leqslant$ $3abc$

Solving $(x^2+4x+3)^x+(2x+4)^x=(x^2+4x+5)^x$ with $x\in(-1,\infty)$

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