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Mathematics-Online problems:

Interactive Problem 143: Unit Circle inside a Parabola

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The figure shows a circle with radius $ 1$ touching the parabola

$\displaystyle P:\ y = x^2 $

at two points.

\includegraphics[width=.6\linewidth]{TdM_11_A1_bild_en}


Determine the center $ C=(0,c)$ of the circle, the point of tangency $ T=(t,t^2)$ as well as the areas of the two shaded segments $ A_1$ and $ A_2.$


Answer:

$ c = $  
$ t = $  
$ A_1 = $  
$ A_2 = $  

(The results should be correct to four decimal places.)


   

(From: Mathematics Contest 2011)
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  automatically generated: 8/11/2017