This week's maths problem

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Problem of the week

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On Friday of each week we will post a new maths challenge.
You may submit your solution by the following Thursday.
Each problem contains two different levels of difficulty. You will be awarded from 2 to 12 points for a full answer.
Each series contains 12 problems before the stage winner is determined.
Your score will be published here.

In each series we will give away 3 books as prices. The prices will be drawn by lot among the best ten participants of the series. The books are kindly sponsored by Buchdienst Rattei of Chemnitz.

Suggestions for problems are welcome.

Deadline is 13th. February 2025


German version - Italian version - French version - Spanish version  Hungarian Version Russian version  --> 中文/Chinese <-- --> Ελληνικά   <-- Esperanto <-- --> Arabic <--

Series 68

problem 814

 

814

‘The series is slowly coming to an end and there was still no 3-4-5 Pythagoras triangle. That will be changed immediately!’ said Bernd.
The following applies to the triangle shown: b = 3 cm, c= 4 cm a = 5 cm. Point I is the centre of the inscribed circle, S is the centre of gravity of the triangle. Points I, S and E lie on a straight line that is parallel to side c. The straight line through E and F is parallel to side b.
What are the area and perimeter of the blue triangle FBE? 5 blue points
Is there another larger right-angled triangle ABC in which the straight line through I and S is parallel to side c? The side lengths should be integers and the triangle you are looking for and the given triangle should not be similar to each other.
There are 8 red points for finding such a triangle or showing that such a triangle cannot exist.

Deadline for solution is the 13th. February 2025.

 


 


-> Enigma <--

https://www.schulmodell.eu/images/stories/mathe/horst/raetsel.php

 

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adress:
Thomas Jahre
Paul-Jäkel-Straße 60
09113 Chemnitz
Germany


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post address:

Thomas Jahre
Chemnitzer Schulmodell
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09119 Chemnitz
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