Question

if all vertices of the quadrilateral lie on the same circle then the quadrilateral is cyclic quadrilateral prov fast PLZZZZZZZZZZ​

Answer 1

Answer:

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. The center of the circle and its radius are called the circumcenter and the circumradius respectively. Other names for these quadrilaterals are concyclic quadrilateral and chordal quadrilateral, the latter since the sides of the quadrilateral are chords of the circumcircle. Usually the quadrilateral is assumed to be convex, but there are also crossed cyclic quadrilaterals. The formulas and properties given below are valid in the convex case.

The word cyclic is from the Ancient Greek κύκλος (kuklos) which means "circle" or "wheel".

All triangles have a circumcircle, but not all quadrilaterals do. An example of a quadrilateral that cannot be cyclic is a non-square rhombus. The section characterizations below states what necessary and sufficient conditions a quadrilateral must satisfy to have a circumcircle.

Step-by-step explanation:

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Answer 2

Answer:

so firstly you can draw the diagonals of that quadrilateral and applying the therom of these chapter that is angle subtend by the same chord are equal

solution

angle 1 +angle 2+ 3+4+5+6+7+8=360

2angle 2 + 2 angle+ 2angle 6+2 angle 8 = 360

2(2+4+6+8)=360

2+4+6+8=360/2

2+4+6+8=180

HENCE IT IS PROVED

Step-by-step explanation:

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