Find the area of trapezoid circumscribed about a circle?

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Discussion Overview

The discussion revolves around finding the area of a trapezoid that is circumscribed about a circle. Participants explore various approaches to solving the problem, including geometric relationships and properties of tangents and circles. The conversation includes attempts to visualize and break down the trapezoid into simpler shapes for area calculation.

Discussion Character

  • Homework-related
  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in progressing with the problem despite having attempted to create a rectangle within the trapezoid.
  • Another participant suggests breaking the trapezoid into triangles to compute the area, emphasizing that area is additive.
  • There is a mention of the relationship between the radius of the circle and the tangent lines, with a question posed about the properties of these relationships.
  • A hint is provided regarding the equality of lengths of line segments tangent to a circle from a common point.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the method to find the area of the trapezoid. Multiple approaches are discussed, and uncertainty remains regarding the application of geometric properties and relationships.

Contextual Notes

Some participants express confusion about the relationships between angles, tangents, and the radius, indicating potential gaps in understanding these concepts. The discussion also reflects varying levels of familiarity with geometric properties relevant to the problem.

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.
 
Last edited:

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