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1. ### MHB Difference of angles in a triangle

How to use it, because I don;t know :(
2. ### MHB Difference of angles in a triangle

so how to calculate for example angle ABC?
3. ### MHB Difference of angles in a triangle

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...

6. ### MHB Prove Angle of Diagonals in Quadrilateral is Degrees

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
8. ### MHB Prove Angle of Diagonals in Quadrilateral is Degrees

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.

10. ### MHB Find the angle in the triangle

Maybe you have GDC=7x? we at home :)
11. ### MHB Find the angle in the triangle

$\triangle CGD$ is not also isosceles. If only we could prove that $\triangle CGD$ is similar to $\triangle AGC$, if GDC=7x ??
12. ### MHB Find the angle in the triangle

Look page 74.
13. ### MHB Find the angle in the triangle

This is the problem with the 4 point kangaroo competition.
14. ### MHB Find the angle in the triangle

But that equation is hard to solve.
15. ### MHB Find the angle in the triangle

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.

17. ### MHB Find the angle in the triangle

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

20. ### MHB Find the angle in the triangle

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?
21. ### MHB Proving $\angle ABC$ is Acute: Inside the Triangle $ABC$

@topsquark Why doesn't the triangle fit the criteria? This triangle fits the criteria.
22. ### MHB Proving $\angle ABC$ is Acute: Inside the Triangle $ABC$

Inside the triangle $ABC$ is point $P$, such that $BP > AP$ and $BP > CP$. Prove that $\angle ABC$ is acute.
23. ### MHB Area of Square ABCD: 6

Solution pure geometry:

Hint:
25. ### MHB Area of Square ABCD: 6

Find area of square ABCD if OQ=OF=6.
26. ### MHB Inequality in triangle

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...
29. ### MHB Find $\angle B$ for Triangle $ABC$ with Bisectors $AD,BE$

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 $AB+BD=AE+BE.$
30. ### MHB Parallelograms in a hexagon

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.
31. ### MHB Number of Solutions

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

:
33. ### MHB Solving $\tan^2x + \tan^2{2x} + \cot^2{3x} = 1$ in R

Show that it doesn't have a solution.
34. ### MHB Solving $\tan^2x + \tan^2{2x} + \cot^2{3x} = 1$ in R

But without desmos etc.
35. ### MHB Solving $\tan^2x + \tan^2{2x} + \cot^2{3x} = 1$ in R

Solve in R $\tan^2x + \tan^2{2x} + \cot^2{3x} = 1$.
36. ### MHB Counting Color Combinations in 12 Triangles

Almost right :)
37. ### MHB 1.4.1 complex number by condition

a+bi=10 a=10 b=0
38. ### MHB Area of Triangle ABC Given Dimensions

This is what it looks like, but how to justify the red ones or maybe there is another way?
39. ### MHB Area of Triangle ABC Given Dimensions

In triangle ABC $AC=BD, CE=2, ED=1, AE=4$ and $\angle CAE=2 \angle DAB$. Find area ABC.
40. ### MHB Counting Color Combinations in 12 Triangles

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.
43. ### MHB Adam's Circles: Splitting & Connecting Segments

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...

45. ### MHB Geom Ch: Prove $AB=x^3$ Given $\triangle ABC$ & $\triangle AEF$

https://www.hostpic.org/images/2107161424150121.png
46. ### MHB Calculating $2\sqrt{2}$ to Infinity

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}
47. ### MHB Calculating $2\sqrt{2}$ to Infinity

If you want: calculate $2\ \cdot \ \sqrt{2\sqrt{2\sqrt{2\sqrt{2 \cdots}}}}$. 2 * "that sqrts"

14,17,...
49. ### MHB Prove Inequality x,y with $x+y=2$

Let x,y>0 and x+y=2. Prove $\sqrt{x+\sqrt{y^2+7}}+\sqrt{y+\sqrt{x^2+7}}\geq2\sqrt3$
50. ### MHB Calculating $2\sqrt{2}$ to Infinity

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