MathDB

3

Part of 2011 May Olympiad

Problems(2)

starting with a right triangle, angles between two lines wanted

Source: May Olympiad (Olimpiada de Mayo) 2011 L2

9/11/2018
In a right triangle rectangle ABCABC such that AB=ACAB = AC, MM is the midpoint of BCBC. Let PP be a point on the perpendicular bisector of ACAC, lying in the semi-plane determined by BCBC that does not contain AA. Lines CPCP and AMAM intersect at QQ. Calculate the angles that form the lines APAP and BQBQ.
geometryright triangleisoscelesangleperpendicular bisector
area inside a rectangle (May Olympiad 2011 L1)

Source:

5/11/2019
In the rectangle ABCD,BC=5,EC=1/3CDABCD, BC = 5, EC = 1/3 CD and FF is the point where AEAE and BDBD are cut. The triangle DFEDFE has area 1212 and the triangle ABFABF has area 2727. Find the area of the quadrilateral BCEFBCEF . https://1.bp.blogspot.com/-4w6e729AF9o/XNY9hqHaBaI/AAAAAAAAKL0/eCaNnWmgc7Yj9uV4z29JAvTcWCe21NIMgCK4BGAYYCw/s400/may%2B2011%2Bl1.png
geometryrectanglearea of a triangleareas