A New Proof of Yun’s Inequality for Bicentric Quadrilaterals
نویسندگان
چکیده
We give a new proof of a recent inequality for bicentric quadrilaterals that is an extension of the Euler-like inequality R ≥ √ 2r. A bicentric quadrilateral ABCD is a convex quadrilateral that has both an incircle and a circumcircle. In [6], Zhang Yun called these “double circle quadrilaterals” and proved that
منابع مشابه
On a Circle Containing the Incenters of Tangential Quadrilaterals
When we fix one side and draw different tangential quadrilaterals having the same side lengths but different angles we observe that their incenters lie on a circle. Based on a known formula expressing the incircle radius of a tangential quadrilateral by its tangent lengths, some older results will be presented in a new light and the equation of the before mentioned circle will appear. This circ...
متن کاملCharacterizations of Bicentric Quadrilaterals
We will prove two conditions for a tangential quadrilateral to be cyclic. According to one of these, a tangential quadrilateral is cyclic if and only if its Newton line is perpendicular to the Newton line of its contact quadrilateral.
متن کاملMaximal Area of a Bicentric Quadrilateral
We prove an inequality for the area of a bicentric quadrilateral in terms of the radii of the two associated circles and show how to construct the quadrilateral of maximal area.
متن کاملA New Proof of Menelaus’s Theorem of Hyperbolic Quadrilaterals in the Poincaré Model of Hyperbolic Geometry
In this study, we present a proof of the Menelaus theorem for quadrilaterals in hyperbolic geometry, and a proof for the transversal theorem for triangles.
متن کاملextend numerical radius for adjointable operators on Hilbert C^* -modules
In this paper, a new definition of numerical radius for adjointable operators in Hilbert -module space will be introduced. We also give a new proof of numerical radius inequalities for Hilbert space operators.
متن کامل