This week's maths problem

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 14th of December 2017.

German version - Italian version - French version - Spanish version

 

Series 46

problem 552

552

“Look, I constructed this green circle (M_2) inside the grey circle (M_1, r= 9 cm). The white angle at M_1 is 60°. The green circle touches the angle in points D and A.”, Lisa explained to Mike.
“Just as well you chose 60° for the angle, that makes the radius of the green circle quite easy to guess.”
What is the radius of the green circle and how can the green circle be constructed (without measuring). Give a description. - 2 + 3 blue points
For red: Let the white angle be 90°. How big would the radius of the green circle have to be and how could this circle be constructed. Full description – 5 red points.
Note: The total sum of 10 possible points can also be attained for positioning the grey circle in a coordinate system and (M_1 (0;0), 01 = 1cm) and giving the coordinates of M_2 and the radii as function of the angles between 0° and 90°. 

               


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adress:
Thomas Jahre
Stollberger Strasse 25
09119 Chemnitz
Germany


Links:

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post address:

Thomas Jahre
Chemnitzer Schulmodell
Stollberger Straße 25
09119 Chemnitz
Deutschland/Germany
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