# Thread: The shapes of things to come...

1. ## Re: The shapes of things to come...

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">16/3 or 5 1/3</span hide>

2. ## The shapes of things to come...

In the diagram, the larger circle <font color=008080> A </font color=008080> has a radius of <font color=008080> 4 </font color=008080> and center point <font color=008080> e </font color=008080>.
The smaller circles <font color=008080> B </font color=008080> & <font color=008080> R </font color=008080> are drawn inside of circle <font color=008080> A </font color=008080> so that all three are mutually tangent ( <font color=008080> B </font color=008080> & <font color=008080> R </font color=008080> intersect at <font color=008080> e </font color=008080>).
Let <font color=008080> b </font color=008080> indicate the center point of circle <font color=008080> B </font color=008080>.
Circle <font color=008080> D </font color=008080> (with center point <font color=008080> d </font color=008080>) is tangent to circles <font color=008080> A </font color=008080>, <font color=008080> B </font color=008080> & <font color=008080> R </font color=008080>.
Circle <font color=008080> C </font color=008080> (with center point <font color=008080> c </font color=008080>) is tangent to <font color=008080> A </font color=008080>, <font color=008080> B </font color=008080> & <font color=008080> D </font color=008080>.

<font face="Comic Sans MS"> Q. What is the area of the quadrilateral edcb? </font face=comic>
Note: The drawing (used for illustration purposes) is not guaranteed precise or accurate. Do not automatically assume that the shaded region is a parallelogram or a rectangle...

3. ## Re: The shapes of things to come...

Would like to see your approach to solving this one...

4. ## Re: The shapes of things to come...

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Say the radius of circle D is r.
Because of the symmetry, de is perpendicular to be.
Pythagoras theorem for triangle bde says bd

5. ## Re: The shapes of things to come...

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">I began by drawing a line from b to d and using Pythagoras also. I ended up with the correct solution, but only under the assumption that the quadrilateral was a rectangle. I was unable to prove that the shaded region was a truly a rectangle. While constructing the drawing, it was somewhat apparent. Your solution was helpful in that it also proved the rectangle...</span hide>

<img src=/S/cheers.gif border=0 alt=cheers width=30 height=16>

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