MathDB

2019.7

Part of Croatia MO (HMO) - geometry

Problems(1)

min AB: CD wanted, diagonals AC, BD bisect DX, CX respectively in cyclic ABCD

Source: 2019 Croatia MO p7

8/2/2020
On the side ABAB of the cyclic quadrilateral ABCDABCD there is a point XX such that diagonal ACAC bisects the segment DXDX, and the diagonal BDBD bisects the segment CXCX. What is the smallest possible ratio ∣AB∣:∣CD∣|AB | : |CD| in such a quadrilateral ?
ratiogeometryCyclicbisects segmentcyclic quadrilateral