bicentric वाक्य
उदाहरण वाक्य
मोबाइल
- All triangles and all regular polygons are bicentric.
- For a tangential quadrilateral with given sides, the inradius is cyclic ( and hence a bicentric quadrilateral ).
- For the circumradius-to-inradius ratio for various " n ", see Bicentric polygon # Regular polygons.
- For an ex-tangential quadrilateral with given sides, the exradius is cyclic ( and hence an ex-bicentric quadrilateral ).
- This strict definition excludes pairs of bicentric points such as the Brocard points ( which are interchanged by a mirror-image reflection ).
- On the other hand, a rectangle with unequal sides is not bicentric, because no circle can be tangent to all four sides.
- The four sides of a bicentric quadrilateral are the four solutions of a quartic equation parametrized by the semiperimeter, the inradius, and the circumradius.
- Note that the converse does not hold : Some quadrilaterals that are not bicentric also have area \ displaystyle K = \ sqrt { abcd }.
- Several binary operations, such as midpoint and trilinear product, when applied to the two Brocard points, as well as other bicentric pairs, produce triangle centers.
- If a polygon is both tangential and cyclic, it is called bicentric . ( All triangles are bicentric, for example . ) The incentre and circumcentre of a bicentric polygon are not in general the same point.
- If a polygon is both tangential and cyclic, it is called bicentric . ( All triangles are bicentric, for example . ) The incentre and circumcentre of a bicentric polygon are not in general the same point.
- If a polygon is both tangential and cyclic, it is called bicentric . ( All triangles are bicentric, for example . ) The incentre and circumcentre of a bicentric polygon are not in general the same point.
- If two circles, one within the other, are the incircle and the circumcircle of a bicentric quadrilateral, then every point on the circumcircle is the vertex of a bicentric quadrilateral having the same incircle and circumcircle.
- If two circles, one within the other, are the incircle and the circumcircle of a bicentric quadrilateral, then every point on the circumcircle is the vertex of a bicentric quadrilateral having the same incircle and circumcircle.
- Fuss's theorem, which is a generalization of Euler's theorem in geometry to a bicentric quadrilateral, says that if a quadrilateral is bicentric, then its two associated circles are related according to the above equations.
- Fuss's theorem, which is a generalization of Euler's theorem in geometry to a bicentric quadrilateral, says that if a quadrilateral is bicentric, then its two associated circles are related according to the above equations.
- The first and second Brocard points are one of many bicentric pairs of points, pairs of points defined from a triangle with the property that the pair ( but not each individual point ) is preserved under similarities of the triangle.
- In a bicentric quadrilateral, the inradius " r ", the circumradius " R ", and the distance " x " between the incenter and the circumcenter are related by Fuss'theorem according to
- In geometry, a "'bicentric polygon "'is a tangential polygon ( a polygon all of whose sides are tangent to an inner incircle ) which is also outer circle that passes through each vertex of the polygon.
- Since " eg " = " fh " if and only if the tangential quadrilateral is also cyclic and hence bicentric, this shows that the maximal area \ sqrt { abcd } occurs if and only if the tangential quadrilateral is bicentric.
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