Find the area of trapezoid circumscribed about a circle?

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SUMMARY

The discussion focuses on calculating the area of a trapezoid that is circumscribed about a circle. Participants emphasize the importance of breaking down the trapezoid into triangles to compute the area effectively. Key insights include the relationship between the radius and tangent of the circle, specifically that the radius and tangent are perpendicular at any point on the circle. The discussion highlights the necessity of understanding geometric properties and relationships to solve the problem accurately.

PREREQUISITES
  • Understanding of trapezoidal geometry
  • Knowledge of triangle area calculation
  • Familiarity with the properties of circles, specifically radius and tangent relationships
  • Basic skills in geometric problem-solving
NEXT STEPS
  • Study the properties of trapezoids and their relationship with inscribed circles
  • Learn how to calculate the area of triangles formed within complex shapes
  • Research the geometric relationship between radius and tangent lines
  • Explore advanced geometric problem-solving techniques, including area decomposition
USEFUL FOR

Students studying geometry, mathematics educators, and anyone interested in solving complex geometric problems involving trapezoids and circles.

Yuki
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Hello, I have encounted this problem and really need some help =/
The figure is attached. Or you can view it in here: http://img404.imageshack.us/img404/1120/mathhelpppp6yk.gif"

Thanks a lot, really urgent :frown:
 

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What figures can you compute the area of?
Can you find those figures in this diagram? (Remember, area is additive.)
How would you use information about the circle?
 
I have tried to create a rectangle inside that trapezoid, which is from point D and C down to the bottom line. Even though so =s I still can't keep moving =s I note the angle thing on the trapezoid. But like, I also tried to see if I can figure out the degree of Angle CBA or DAB Yet I still get stucked =( I don't know what I am missing to move to next step =/
Thanks for the fast reply
 
Can you find the area of a triangle?
Do you know the relationship between a radius and a tangent?
 
I know how to find the area of a triangle. However, many triangles can be formed in there =/ So I am kinda lost =s I know radius and tangent, however I never learned any relationship between raidus and tangent
Thanks a lot for help!
 
If you can break up your figure into triangles, and you can find the areas of those triangles, then you can add these areas to get the area of the whole figure.

Do you know that at any point on the circle, the radius and tangent-line are perpendicular?
 
Here is a hint:

If two line segments share a common endpoint p, and are each tangent to a circle at their opposite endpoints, they have the same length.
 
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