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equal sums of 2 sides, cyclic ABCD, <BAD = 60^o, AO = 3OC

Source: 2012 All-Ukrainain Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p10

April 26, 2021

geometryequal segmentscyclic quadrilateralUkraine Correspondence

Problem Statement

The diagonals

AC

and

BD

of the cyclic quadrilateral

ABCD

intersect at a point O. It is known that

\angle BAD = 60^o

and

AO = 3OC

. Prove that the sum of some two sides of a quadrilateral is equal to the sum of the other two sides.