MathDB

Area/(Perimeter)^2 of cyclic quadrilateral

Source: Turkey TST 1999 - P4

July 2, 2012

geometryperimetercircumcirclecyclic quadrilateralgeometry proposed

Problem Statement

Let the area and the perimeter of a cyclic quadrilateral

C

A_C

and

P_C

, respectively. If the area and the perimeter of the quadrilateral which is tangent to the circumcircle of

C

at the vertices of

C

are

A_T

and

P_T

, respectively, prove that

\frac{A_C}{A_T} \geq \left (\frac{P_C}{P_T}\right )^2