MathDB

12

Part of 2022 CMIMC

Problems(1)

2022 Team P12

Source:

2/28/2022
Let ABCDABCD be a cyclic quadrilateral with AB=3,BC=2,CD=6,DA=8,AB=3, BC=2, CD=6, DA=8, and circumcircle Γ.\Gamma. The tangents to Γ\Gamma at AA and CC intersect at PP and the tangents to Γ\Gamma at BB and DD intersect at Q.Q. Suppose lines PBPB and PDPD intersect Γ\Gamma at points W≠BW \neq B and X≠D,X \neq D, respectively. Similarly, suppose lines QAQA and QCQC intersect Γ\Gamma at points Y≠AY \neq A and Z≠C,Z \neq C, respectively. What is the value of WX2YZ2?\frac{{WX}^2}{{YZ}^2}?
Proposed by Kyle Lee
team