Finding diagonal of inscribed rectangle

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Homework Help Overview

The problem involves a rectangle inscribed in a quadrant of a circle, with a specific distance given for one side. The objective is to determine the length of another side based on the properties of the rectangle and the circle.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the sides of the rectangle and the properties of its diagonals, questioning the reasoning behind the equality of certain lengths.

Discussion Status

The discussion is exploring the properties of rectangles, particularly focusing on the equality of diagonals. Participants are confirming the correctness of the original poster's understanding while seeking deeper reasoning behind the relationships presented.

Contextual Notes

There is an implicit assumption regarding the properties of rectangles and their diagonals, as well as the relationship between the rectangle and the inscribed circle. The specific dimensions of the rectangle and the radius of the circle are also relevant but not fully detailed.

Ein Krieger
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Homework Statement


A quadrant contains an inscribed rectangle ABCD. Given the distance marked: CD=3m , what is length of AD?




Homework Equations



Area of circle = pi*r^2
Pythagorean 's theorem : a^2=b^2+c^2

The Attempt at a Solution



We can draw diagonal from C to B similar to that from A to D. And that diagonal is equal to radius which is 10. Correct?
 
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Correct. Do you know the reason it is correct? I mean, what is the reason that CB = AD?
 
verty said:
Correct. Do you know the reason it is correct? I mean, what is the reason that CB = AD?

be cause it is a rule for all rectangles?
 
Yes indeed. The diagonals of a rectangle are equal. A rhombus and parallelogram do not have equal diagonals, this is special to a rectangle.
 

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