MathDB

S = \sqrt{abcd}, area of bicentric

Source: Polish MO second round 1952 p2

August 28, 2024

geometryareas

Problem Statement

Prove that if

a

b

c

d

are the sides of a quadrilateral in which a circle can be circumscribed and a circle can be inscribed in it, then the area

S

of the quadrilateral is given by

S = \sqrt{abcd}.