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`        show that all the rectangles of maximum perimeter which can be inscribed in a circle of radius 'a' is square of side root2a`
7 years ago

SAGAR SINGH - IIT DELHI
879 Points
```										Dear girvinder,
The largest rectangle would be a square. If the circle has radius a, the  diameter is 2a. This diameter would also be the diameter of a square of  side length b. Using the Pythagorean theorem, b2 + b2 = (2a)2.  2b2 = 4a2 b2 = 2a2 b = √(2a2) or a√2 = the length of the sides of the square  The area of a square of side length b is therefore (√(2a2))2 = 2a2 which is the largest area for a rectangle inscribed in a circle of radius a.

We are all  IITians and here to help you in your IIT  JEE preparation.  All the best.

Sagar Singh
B.Tech IIT Delhi

```
7 years ago
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