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 24th August 2017.

German version - Italian version - French version - Spanish version

 

Series 45

problem 538


538

“Again you've drawn circles”, Mike said.
“That's right, but I think there also is a magic circle.”, Lisa replied.
Circles k1 and k2 touch each other in point A. Points B and D are touching points with tangent h. Tangents h and f meet in point C.
If the radii of the circles are equal (4 cm), points B, D, M2 and M1 make a rectangle. What is the percentage of the white are of this rectangle? - 4 blue points.
4 red points for proving that A, B and D will always be part of a circle centered in C, no matter how big the other circles are.
Another 4 red points for calculating the angles at point C if the radius of k2 is twice the radius of k1.
 


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You can also send a paper copy of your solution as long as it is postmarked on or before the deadline.
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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Kommentare   

+3 #1 Cora 2014-11-13 23:03
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