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In a cyclic quadrilateral ABCD, <ABC=120 degrees

Source: Indian National Maths Olympiad, Problem 5

February 5, 2006

trigonometryinequalitiesfunctiongeometrycircumcirclecyclic quadrilateralgeometry proposed

Problem Statement

In a cyclic quadrilateral

ABCD

AB=a

BC=b

CD=c

\angle ABC = 120^\circ

and

\angle ABD = 30^\circ

. Prove that (1)

c \ge a + b

; (2)

|\sqrt{c + a} - \sqrt{c + b} | = \sqrt{c - a - b}