Hello, aldrincabrera!

i was proving "Are circumscribable quadrilaterals always inscribable?"

and i found out that they are not ... it only happens for certain conditions.

But my teacher ask me the other way around. .Now i am having a hard time

proving "Are inscribable quadrilaterals always circumscribable?"

Can anyone please help me with the proof?

The answer to both questions is "No."

No proof is required . . . just a counterexample.

I assume a "circumscribable quadriateral" is one which can be circumscribed.

. . That is, it can be inscribed in a circle.

Code:

* * *
A o-----------o B
*/ \*
*/ \*
/ \
D o-------------------o C
* *
* *
* *
* *
* *
* * *

Quadrilateral $\displaystyle ABCD$ is circumscribable.

But no circle can be inscribed within it.

Code:

A o---*-*-*---------------o B
/* * /
* * /
* * /
/ /
/* * /
/ * * /
/ * */
/ /
/ * *
/ * *
/ * */
D o---------------*-*-*---o C

Quadrilateral $\displaystyle ABCD$ is inscribable.

But no circle can be circumscribed around it.

. . (In this case it is, after all, a rhombus.)

In fact, the only quadrilateral which is inscribable

. . *and* circumscribable is a *square*.