each vertex of the hexagon lies outside the circle
the hexagon is circumscribed about the circle
the vircle is tangent to each side of the hexagon
Yes. The corners must be right angles for it to be inscribed on the circle.
True.
hexagon
An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle.The other two endpoints define an intercepted arc on the circle Any angle inscribed in a semi-circle is a right angle. The proof is simply that the intercepted arc is 180 so the angle must be half of that or 90 degrees.
They must be congruent.
If a parallelogram is inscribed in a circle then it must be a cyclic quadrilateral.
Yes. The corners must be right angles for it to be inscribed on the circle.
Yes, a parallelogram inscribed in a circle must be a rectangle. This is because a circle's inscribed angle theorem states that the opposite angles of a cyclic quadrilateral (a quadrilateral inscribed in a circle) must be supplementary. In a parallelogram, opposite angles are equal, which can only hold true if all angles are right angles, thus making the parallelogram a rectangle.
True.
hexagon
No, because there is no acute angle in a circle.
yes ...all the angles of the triangle must touch a spot on the circle..
There is only one possible circle that can be inscribed in any triangle because all of the sides of the triangle must touch the circle at some point. Also, there is only one "incenter" of each circle. The incenter is the center of an inscribed circle.
An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle.The other two endpoints define an intercepted arc on the circle Any angle inscribed in a semi-circle is a right angle. The proof is simply that the intercepted arc is 180 so the angle must be half of that or 90 degrees.
They must be congruent.
This statement is incorrect. To circumscribe a circle around a triangle, the circle's center must be located at the circumcenter, not the incenter. The circumcenter is the point where the perpendicular bisectors of the triangle's sides intersect, while the incenter is the point where the angle bisectors meet and is the center of the triangle's inscribed circle.
Yes. A hexagon must have an obtuse angle.