चक्रीय चतुर्भुज: Difference between revisions
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[[File:Cyclic quadrilateral.jpg|alt=Fig. 1|thumb| | [[File:Cyclic quadrilateral.jpg|alt=Fig. 1|thumb|चित्र -1]] | ||
A quadrilateral ABCD is called cyclic if all the four vertices | A quadrilateral ABCD is called cyclic if all the four vertices | ||
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the quadrilateral is cyclic. | the quadrilateral is cyclic. | ||
== | == उदाहरण == | ||
[[File:Cyclic quadrilateral - 2.jpg|alt=Fig. 2|thumb| | [[File:Cyclic quadrilateral - 2.jpg|alt=Fig. 2|thumb|चित्र -2]] | ||
1: In Fig 2, <math>ABCD</math> is a cyclic quadrilateral in which <math>AC</math> and <math>BD</math> are its diagonals. | 1: In Fig 2, <math>ABCD</math> is a cyclic quadrilateral in which <math>AC</math> and <math>BD</math> are its diagonals. | ||
Revision as of 07:16, 11 September 2024
A quadrilateral ABCD is called cyclic if all the four vertices
of it lie on a circle (see Fig 1).
Here we find that and .
Theorems related to Cyclic Quadrilateral are mentioned below.
Theorem 1: The sum of either pair of opposite angles of a cyclic quadrilateral
is .
Theorem 2: If the sum of a pair of opposite angles of a quadrilateral is ,
the quadrilateral is cyclic.
उदाहरण
1: In Fig 2, is a cyclic quadrilateral in which and are its diagonals.
If and , find
Solution:
(Angles in the same segment)
Therefore,
But (Opposite angles of a cyclic quadrilateral)