Finding diagonal of inscribed rectangle

AI Thread Summary
In a quadrant containing an inscribed rectangle ABCD, the length of side AD is determined by the diagonal CB, which equals the radius of the circle at 10m. The relationship between the sides is confirmed by the property that the diagonals of a rectangle are equal. The distance CD is given as 3m, leading to a discussion on the application of the Pythagorean theorem to find the dimensions of the rectangle. The conversation emphasizes that while rectangles have equal diagonals, this property does not apply to other quadrilaterals like rhombuses or parallelograms. Understanding these geometric properties is essential for solving related problems.
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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