# Thread: Drawing Circumscribable Quadrilateral which is at the same time inscribable,

1. ## Drawing Circumscribable Quadrilateral which is at the same time inscribable,

,.,good day,.,amm,.,.how should i draw a quadrilateral which is circumscribable and at the same time inscribable??can u give me examples with measures???thnx a lot

2. ## Re: Drawing Circumscribable Quadrilateral which is at the same time inscribable,

please explain what exactly you wants to know, every square can be circumscribed and inscribed

3. ## Re: Drawing Circumscribable Quadrilateral which is at the same time inscribable,

,.,.i want to know about what it looks like in other quadrilaterals aside from square,.,.

4. ## Re: Drawing Circumscribable Quadrilateral which is at the same time inscribable,

Originally Posted by aldrincabrera
,.,.i want to know about what it looks like in other quadrilaterals aside from square,.,.
The general case of a quadrilateral which has an incircle and a circumscribed circle is a symmetric trapezium whose slanted side is as long as it's mid-parallel.

This case includes squares.

5. ## Re: Drawing Circumscribable Quadrilateral which is at the same time inscribable,

The condition for the quadrilateral to be circumscribable (by a circle) is that both pairs of opposite angles should add up to 180°. The condition for it to be inscribable is that the sum of the lengths of both pairs of opposite sides should be the same. Put those two conditions together and I guess you have the condition given by earboth.

6. ## Re: Drawing Circumscribable Quadrilateral which is at the same time inscribable,

just like drawn in attached jpeg file.

7. ## Re: Drawing Circumscribable Quadrilateral which is at the same time inscribable,

In fact, you can choose any four lengths a, b, c, d satisfying a+c = b+d, and there will be a quadrilateral having those four lengths for its sides which is both inscribable and circumscribable. If the vertices are A, B, C, D, with AB = a, BC = b, CD = c and DA = d, then the length x of the diagonal AC is given by

$\boxed{x^2 = \frac{(ac+bd)(ad+bc)}{ab+cd}}.$

Once you know x, it is easy to draw the quadrilateral. For example, if a=3, b=4, c=6, d=5, then $x\approx5.94$ and the quadrilateral looks like the picture below. (The incircle is not exactly located, because I was guessing the position of its centre and didn't get it quite right.)