MathDB

2.4

Part of 2011 Saudi Arabia Pre-TST

Problems(2)

SM//CL wanted, ABCD rectangle , <DAC = 60^o

Source: 2011 Saudi Arabia Pre-TST November 2.4

12/31/2021
Let ABCDABCD be a rectangle of center OO, such that ∠DAC=60o\angle DAC = 60^o. The angle bisector of ∠DAC\angle DAC meets DCDC at SS. Lines OSOS and ADAD meet at LL and lines BLBL and ACAC meet at MM. Prove that lines SMSM and CLCL are parallel.
geometryrectangleparallel
triangle of medians of ABC similar to ABC criterion

Source: 2011 Saudi Arabia Pre-TST February 2.4 https://artofproblemsolving.com/community/c2745403_2011_

1/1/2022
Let ABCABC be a triangle with medians mam_a , mbm_b, mcm_c. Prove that: (a) There is a triangle with side lengths mam_a ,mbm_b, mcm_c. (b) This triangle is similar to ABCABC if and only if the squares of the side lengths of triangle ABCABC form an arithmetical sequence.
similar trianglesgeometryMediansmedian