MathDB

2

Part of 2023 Rioplatense Mathematical Olympiad

Problems(2)

Perpendicular Likers Go on

Source: Rioplatense L3 2023 #2

12/6/2023
Let ABCDABCD be a convex quadrilateral with AB>ADAB>AD and ∠B=∠D=90∘\angle B=\angle D=90^{\circ}. Let PP be a point in the side ABAB such that AP=ADAP=AD. The lines PDPD and BCBC cut in the point QQ. The perpendicular line to ACAC passing by QQ cuts ABAB in the point RR. Let SS be the foot of perpendicular of DD to the line ACAC. Prove that ∠PSQ=∠RCP\angle PSQ=\angle RCP.
geometry
geometry rioplatense MO 2023 P2

Source: Rioplatense L-2 2023 #2

12/5/2023
Let ABCDABCD be a convex quadrilateral, such that AB=CDAB = CD, ∠BCD=2∠BAD\angle BCD = 2 \angle BAD, ∠ABC=2∠ADC\angle ABC = 2 \angle ADC and ∠BAD≠∠ADC\angle BAD \neq \angle ADC. Determine the measure of the angle between the diagonals ACAC and BDBD.
geometryexcenterAngle Chasing