High School Math geometry

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Geometry

Exoticbuttersowo 1

N 2 hours ago by sunken rock

In an isosceles triangle ABC with base AC and interior cevian AM, such that MC = 2 MB, and a point L on AM, such that BLC = 90 degrees and MAC = 42 degrees. Determine LBC.

1 reply

Exoticbuttersowo

Yesterday at 7:28 PM

sunken rock

2 hours ago

J

H

Pure algebra problem

lgx57 1

N 2 hours ago by HAL9000sk

If $a_0=5$ , $a_n=a_{n-1}+\dfrac{1}{a_{n-1}}$ . Let $S=a_{1000}$
Calculate $S$ .

PS1: The more precise decimal places there are, the better.(rounded down)
PS2: Please don't use python or C++, or this problem will be very easy.

1 reply

lgx57

5 hours ago

HAL9000sk

2 hours ago

J

H

Counting problem

lgx57 1

N 3 hours ago by HAL9000sk

Calculate the number of $n$ that meet the following conditions:
1. $585 \mid n$
2. $0 \sim 7$ appears exactly once in each octal digit of $n$

1 reply

lgx57

5 hours ago

HAL9000sk

3 hours ago

J

H

Geometry

Arytva 0

4 hours ago

Let $ABC$ be an acute triangle, and let its circumcircle be $\Gamma$ . On side $BC$ , pick a point $D$ (distinct from $B$ and $C$ ). The lines through $D$ tangent to $\Gamma$ (other than $DA$ , if $A$ lies inside the angle at $D$ ) touch $\Gamma$ again at points $E$ and $F$ . Let $BE$ meet $AC$ at $P$ , and let $CF$ meet $AB$ at $Q$ . Prove that the three lines $AP$ , $AQ$ , and $EF$ are concurrent.

0 replies

Arytva

4 hours ago

0 replies

J

H

Easy Function

Darealzolt 1

N 5 hours ago by alexheinis

Let $f(x+y) = f(x^2y)$ for all real numbers $x,y$ , hence find the value of $f(3)$ if $f(2023)=26$ .

1 reply

Darealzolt

5 hours ago

alexheinis

5 hours ago

J

H

Spot-It inspired question

alexroberts 1

N Today at 6:25 AM by alexroberts

Oscar bought a set of blank playing cards. He puts stamps on each card such that
1. Each card has $k\geq 4$ different stamps each.
2. Every two cards have exactly one stamp in common.
3. Every stamp is used at least twice.

Show that the maximum number of different stamps $v$ he can use is in the range $k^2-2k+5 \leq v \leq k^2-k+1$

1 reply

alexroberts

Wednesday at 8:46 PM

alexroberts

Today at 6:25 AM

J

H

Floor of Cube Root

Magdalo 2

N Today at 6:18 AM by RedFireTruck

Find the amount of natural numbers $n<1000$ such that $\lfloor \sqrt[3]{n}\rfloor\mid n$ .

2 replies

Magdalo

Jun 2, 2025

RedFireTruck

Today at 6:18 AM

J

H

Find the value of m

Darealzolt 2

N Today at 6:13 AM by RedFireTruck

Let $m$ be a positive integer, such that $m$ fulfills
$\frac{1}{m^2+3m+2}+\frac{1}{m^2+5m+6}+\frac{1}{m^2+7m+12}+\dots +\frac{1}{m^2+15m+56}+\frac{1}{m^2+17m+72} = \frac{8}{33}$ Hence find the value of $m$ .

2 replies

Darealzolt

Yesterday at 11:38 AM

RedFireTruck

Today at 6:13 AM

J

H

Polynomials

P162008 2

N Today at 6:02 AM by RedFireTruck

P1. Find $p(0) + p(5)$ where $p$ is a monic polynomial of degree $4$ satisfying $p(r) = 2^r ; r = 1,2,3,4.$

P2. Find $p(1), p(-1)$ where $p$ is a polynomial of smallest degree possible satisfying $p(r) = \frac{1}{r^2 - 1}; r = 2,3,4,\cdots, 10.$

P3. Find $k$ and $p(0)$ , if polynomial $p$ satisfies $x.p(x) + 1 = k\left(\prod_{i = 1}^{5} (x - i)\right).$

P4. Find $p(0)$ where $p$ is a polynomial of smallest degree satisfying $p(r) = \frac{1}{r}; r = 1,2,3,\cdots,10.$

P5. Find $p(0),p(6),k$ and $\alpha$ if polynomial $p$ satisfies $(x^2 - 6x).p(x) + 1 = k\left(\prod_{i=1}^{5} (x - i)\right)(x - \alpha).$

P6. If $f(x)$ is a polynomial of degree $50$ such that $f(x) = \frac{x}{x + 1}; x = 0,1,2,\cdots,50.$ Evaluate $f(-1).$