MathDB

2

Part of 1999 May Olympiad

Problems(2)

Unit circle

Source: May Olympiad (Olimpiada de Mayo) 1999

2/26/2018
In a unit circle where OO is your circumcenter, let AA and BB points in the circle with ∠BOA=90\angle BOA = 90. In the arc ABAB(minor arc) we have the points PP and QQ such that PQPQ is parallel to ABAB. Let XX and YY be the points of intersections of the line PQPQ with OAOA and OBOB respectively. Find the value of PX2+PY2PX^2 + PY^2
geometry
folding a parallelogram, a regular pentagon is constructed, find angles

Source:

5/11/2019
In a parallelogram ABCDABCD , BDBD is the largest diagonal. By matching BB with DD by a bend, a regular pentagon is formed. Calculate the measures of the angles formed by the diagonal BDBD with each of the sides of the parallelogram.
geometryparallelogrampentagonangles