Can anyone help me with this math olympiad task?
(2 votes)
Loading...Similar Posts
Calculate atom number ratio?
What is the atomic number ratio of copper iodide? Please reply
Help with math – growth rate and growth factor?
ByAdam287
Hello everyone, I have a question about this topic. We did some practice exercises in class on growth rate and growth factor, which I mostly understood. However, I'm having a small comprehension issue because in one sub-exercise, I could simply write x%, and in the next exercise, I had to convert x%. (See the following…
[Physics] Derivation of the Lorentz force?
Good day, I still need some help understanding the derivation of the Lorentz force. I'm looking forward to your detailed and easy-to-understand answers. Why do we first solve the formula for the magnetic flux density B (highlighted in green in Figure 2) for Fmag? Can someone explain to me exactly why we start with this?…
Designing microservice architecture – what free software is available for this?
ByJinpachu
I would like to design some architectures. What free software is available for this?
(a) was helpful to see what this is all about 😉
So on with b)
D, E and F are the points of contact of the circle AB, BC or AC.
Angle DAM = angle MAF.
Angle MDA = angle AFM (= 90°).
Since the triangles DMA and MFA have the distance AM and also the incirculation radius r together, they are congruent.
This is followed by AF = AD. (I also know this as a tangent set.)
Also BE = BD.
AF + ME = AF + r = AD + r = a.
(AF and ME are parallel.)
And it is BE + MF = BE + r = BD + r = b.
The sum is AD + BD + 2r = a + b.
Because of AD + BD = c (hypotenuse)
is c + 2r = a + b.
c is at the same time the diameter of the circle, i.e.
2R + 2r = a + b
R + r = (a + b)/2, which was to be proven.
Again very elegant. I am not sure whether you have confused a and b in the meantime (AF + ME = b, BD + r = a), but has no consequences.
That can happen. But if I present the solution of Matheolympiaden tasks, the questioner should urgent check again. 😉