That is the definition of the incenter; it is the center of the inscribed circle.
Yes. The corners must be right angles for it to be inscribed on the circle.
not always, since sometimes kites may have a pair of opposite angles that are not supplementary. Special types of kites can be inscribed.
No, they are supplementary.
An inscribed angle is an angle with its vertex on a circle and with sides that contain chords of the circle.
No, the circle is inscribed in the quadrilateral.
It is an inscribed quadrilateral or cyclic quadrilateral.
The opposite angles of a quadrilateral inscribed in a circle have a sum of 180 degrees.
cyclic
yes
If a parallelogram is inscribed in a circle then it must be a cyclic quadrilateral.
A quadrilateral is inscribed in a circle it means all the vertices of quadrilateral are touching the circle. therefore it is a cyclic quadrilateral and sum of the opposite angles in cyclic quadrilateral is supplementary. suppose if one angle is A then another will be 180 degree - angle A.
if a parallelogram is inscribed in a circle it is always a rectangle...............
No. For example, if one angle measures 100 degrees, and its adjacent angle is 80 degrees, then the opposite angles would be either 200 or 160 degrees, but in order for a quadrilateral to be inscribed in a circle the opposite angles would have to equal 180 degrees. A parallelogram can be inscribed in a circle if it is a rectangle.
There is no specific limitation on any one angle of an inscribed quadrilateral.
That is the definition of the incenter; it is the center of the inscribed circle.
Yes. The corners must be right angles for it to be inscribed on the circle.