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How to use it, because I don;t know :(

so how to calculate for example angle ABC?

In a triangle ABC, let D and E be the intersections of the bisectors of the angles ABC and ACB with the sides AC and AB, respectively. Knowing that the measures in degrees of the angles BDE and CED are equal to 24 and 18, respectively, calculate the difference in degrees between the measures of...

Do you have an answer?

1 / α + β = 90 2 / it is enough to note that the triangles KNP and MLQ (they have two heights of length "a") so they are isosceles so |∡NMQ| =90 - α/2 and |∡MNP| =90 - β/2 γ=(α + β)/2=45

Hint

Two angles of a square with side protrude beyond a strip of width with parallel edges. The sides of the square intersect the edges of the strip at four points. Prove that the diagonals of the quadrilateral whose vertices are these points intersect at an angle of degrees.

Maybe you have GDC=7x? we at home :)

$\triangle CGD$ is not also isosceles. If only we could prove that $\triangle CGD$ is similar to $\triangle AGC$, if GDC=7x ??

Look page 74.

This is the problem with the 4 point kangaroo competition.

But that equation is hard to solve.

Ok but answer is 10 not 0, so how solve this without wolfram. https://hobbydocbox.com/Board_Games_and_Puzzles/77639583-Annual-ksf-meeting-november-protaras-cyprus.html I've tried to find a trick solution.

ADB=180-3x BDC=180-8x ADC=11x ADB + BDC + ADC=180-3x+180-8x+11x=360 And what next??

ok, BAC = 180 - 14x Can you tel why ADB + BDC + ADC= 180? I don't see it.

BAC=180-15x ADB=180-3x BDC=180-8x ADC=11x What next?

I've tried: BC || EF How to find angle GDC? I think GDC=7x but why? I have an answer but how to solve this?

@topsquark Why doesn't the triangle fit the criteria? This triangle fits the criteria.

Inside the triangle $ABC$ is point $P$, such that $BP > AP$ and $BP > CP$. Prove that $\angle ABC$ is acute.

Solution pure geometry:

Hint:

Find area of square ABCD if OQ=OF=6.

Let $x, y, z$ be length of the side of a triangle such that $\sqrt{x} + \sqrt{y} + \sqrt{z} = 1.$ Prove $|x^{2} + y^{2} + z^{2} - 2\left( xy+yz+xz\right)| \le \frac{1}{27}$.

...

Geogebra...

Let $ABC$ be a triangle with $\angle A= 60^{\circ},$ and $AD,BE$ are bisectors of $A,B$ respectively where $D\in BC, E\in AC.$ Find the measure of $B$ if $AB+BD=AE+BE.$

In a convex hexagon $ABCDEF$ exist a point $M$ such that $ABCM$ and $DEFM$ are parallelograms . Prove that exists a point $N$ such that $BCDN$ and $EFAN$ are also parallelograms.

$sin2\theta=x$ $(x + 2) (2 x + 1) (4 x^2 + 7 x + 4) = 0$

:

Show that it doesn't have a solution.

But without desmos etc.

Solve in R $\tan^2x + \tan^2{2x} + \cot^2{3x} = 1$.

Almost right :)

a+bi=10 a=10 b=0

This is what it looks like, but how to justify the red ones or maybe there is another way?

In triangle ABC $AC=BD, CE=2, ED=1, AE=4$ and $\angle CAE=2 \angle DAB$. Find area ABC.

There are 12 triangles (picture). We color each side of the triangle in red, green or blue. Among the $3^{24}$ possible colorings, how many have the property that every triangle has one edge of each color?

It' correct.

Product.

Adam has a circle of radius $1$ centered at the origin. - First, he draws $6$ segments from the origin to the boundary of the circle, which splits the upper (positive $y$) semicircle into $7$ equal pieces. - Next, starting from each point where a segment hit the circle, he draws an...

https://www.hostpic.org/images/2107161424150121.png

No, 2 \sqrt{2} \sqrt{ \Pi _{n = 0}^{\infty} 2^{1/(5 + 3n)} } \neq 2^{1+\frac12+\frac1{2\cdot5}+\frac1{2\cdot5\cdot8}+\frac1{2\cdot5\cdot8\cdot11}+\cdots}

If you want: calculate $2\ \cdot \ \sqrt{2\sqrt[5]{2\sqrt[8]{2\sqrt[11]{2 \cdots}}}}$. 2 * "that sqrts"

14,17,...

Let x,y>0 and x+y=2. Prove $\sqrt{x+\sqrt[3]{y^2+7}}+\sqrt{y+\sqrt[3]{x^2+7}}\geq2\sqrt3$

Calculate $2\sqrt{2\sqrt[5]{2\sqrt[8]{2\sqrt[11]{2 \cdots}}}}$. I know only that $...=2^{1+{1\over2}+{1\over10}+{1\over80}+{1\over880}+\ldots}$