MathDB

3

Part of 2015 May Olympiad

Problems(2)

perpendiculare segments inside a regular 9-gon

Source: May Olympiad (Olimpiada de Mayo) 2015 L2

9/10/2018
Let ABCDEFGHIABCDEFGHI be a regular polygon of 99 sides. The segments AEAE and DFDF intersect at PP. Prove that PGPG and AFAF are perpendicular.
geometryperpendicularregular polygon
Quadrilateral ABCD

Source: May Olympiad(Olimpiada de Mayo) 2015 (junior)

10/10/2017
In the quadrilateral ABCDABCD, we have ∠C\angle C is triple of ∠A\angle A, let PP be a point in the side ABAB such that ∠DPA=90º\angle DPA = 90º and let QQ be a point in the segment DADA where ∠BQA=90º\angle BQA = 90º the segments DPDP and CQCQ intersects in OO such that BO=CO=DOBO = CO = DO, find ∠A\angle A and ∠C\angle C.
geometry