<p>Number 12 page 485, an explanation would be very helpful. None of the tutors on tutorvista.com could help me with this.</p>
<p>I don’t have the book. Can you post the question on here?</p>
<p>It’s pretty easy once you think about it-
The rectangle’s longest side is equivalent to the circle’s diameter, pretty self-explanatory if you’re looking at the diagram.
Now how many set positions are there for a diameter? Infinite. A diameter can be set from top-down, side-side, diagonally, etc. Just like that, you can rotate the rectangles in infinitely small fractions of a degree and it’d fit. Hence, the answer is ‘more than 4’.</p>
<p>If that is the question involving 2 rectangles of perimeter 12, inscribed in the circle then, </p>
<p>Join any two opposite vertices of the rectangle. Let us join, P and R. Then, the diagonal PR is the diameter of the circle since the inscribed angle <PSR is 90. </p>
<p>So, we see that the given rectangles are the ones which have diameter of the circle as their diagonal. Since, there can be infinite no. of diameter lines in a circle, we can draw infinite such rectangle with perimeter 12 ( each having the diameter of the circle as its diagonal).</p>