MathDB

2

Part of 2003 Irish Math Olympiad

Problems(2)

Geometry question

Source:

4/11/2017
PP, QQ, RR and SS are (distinct) points on a circle. PSPS is a diameter and QRQR is parallel to the diameter PSPS. PRPR and QSQS meet at AA. Let OO be the centre of the circle and let BB be chosen so that the quadrilateral POABPOAB is a parallelogram. Prove that BQBQ = BPBP .
geometry
Quadrilateral- feet of the perpendicular

Source:

2/20/2011
 ABCD\ ABCD is a quadrilateral. the feet of the perpendicular from  D\ D to  AB,BC\ AB, BC are  P,Q\ P,Q respectively, and the feet of the perpendicular from  B\ B to  AD,CD\ AD,CD are  R,S\ R,S respectively. Show that if ∠PSR=∠SPQ\angle PSR= \angle SPQ, then  PR=QS\ PR=QS.