aops, Saudi Pre-Test 2011, https://artofproblemsolving.com/community/c6t48f6h2747302_bt__2pt_if_ltbat__lt_bcs__10o_in_40o70o70o_triangle

 

aops, https://artofproblemsolving.com/community/c6t48f6h2745721_ab__mnmn_if_ac__m_ad__n_in_regular_heptagon_abcdefg

 

Geometria Top, Rodrigo Santana Porto, https://www.facebook.com/photo/?fbid=10159887455088304&set=gm.1106716920098676

 

Training Geometry Olympiad (youtube) https://www.youtube.com/watch?v=QkLNGWAnZLM

 

Peru Geometrico, Yusuf Zemzem, https://www.facebook.com/photo?fbid=10220853728806088&set=gm.3318129314966605

 

aops, https://artofproblemsolving.com/community/c4t48f4h2735489_find_the_angle_oie

 Not a nice proof, but synthetical!

Trazo Geometrico Maldito, Geom Airt, https://www.facebook.com/photo/?fbid=447143579772477&set=gm.1061148854397205

 

aops https://artofproblemsolving.com/community/c4t48f4h2734068_prove_that_mi_is_perpendicular_to_bc

 

Tuymaada Junior 2006, https://artofproblemsolving.com/community/c6t48f6h1837994_equal_segments_wanted_starting_with_an_isosceles_and_right_triangle

 

aops, Catalin Bordea, https://artofproblemsolving.com/community/c6t48f6h2731831_suitable_proportion_for_trisecting_the_angle

 

Fake OMA Foros Open, 2017, https://artofproblemsolving.com/community/c6t48f6h2730928_ltbac__2ltabm_if_bc__cd__ac__bd

 

aops, https://artofproblemsolving.com/community/c4t48f4h2730157_calculating_the_angles_of_triangle_kem

 

Pedro Miranda, Training Geometry Olympiad, https://www.facebook.com/photo/?fbid=4533705923372103&set=gm.589447512315566

 

Kazakhstan finals, 2021, https://artofproblemsolving.com/community/c4t48f4h2727784_ltmka_square_abcd_ltbamltckm30o_2nd_matol_202122_kazakhstan_finals_73

 

Geometria Top, Jonathan KY, https://www.facebook.com/photo/?fbid=10215625868479449&set=gm.1094852537951781

 

aops, https://artofproblemsolving.com/community/c4h2719933p23656878

 A metrical solution for this problem: 

Problem, Ali Mohamed Mira, Geometria Top, https://www.facebook.com/photo/?fbid=2103138099840359&set=gm.1090523831717985

 

Problem Geometria Top, Ali Mohamed Mira https://www.facebook.com/photo/?fbid=2105929869561182&set=gm.1092753504828351

 

INMO 2021, problem 5, https://artofproblemsolving.com/community/c4t48f4h2719655_request_for_the_source

 

aops, Cono Sur 2017 Training List, https://artofproblemsolving.com/community/c6t48f6h2723266_ltadb__lt_cam_if_ltdab__90o_ltadc_ltbam

 

aops, Baltic Way SL 2011, https://artofproblemsolving.com/community/c6t48f6h2722119_angle_chasing_ltabd30o__ltcdb__20o_ltbca__lt_acd__40o

 

Generalized problem of Geometria Top, Hajj Mustafa El-Rardini, https://www.facebook.com/photo/?fbid=6710749308942650&set=gm.1087931558643879

A piece of my book, 'Rose thorns - Geometry jewels', I called it 'Triple angle lemma'. The proof is mine.

 

Nelson Tunala, Geometria Top, https://www.facebook.com/photo/?fbid=3907884295946685&set=gm.962288931208143

 

Nelson Tunala, Geometria Top, https://www.facebook.com/photo/?fbid=3914651885269926&set=gm.963789431058093

 

Stanford Li, Training Geometry Olympiad, https://www.facebook.com/photo?fbid=10224737947489560&set=gm.582578046335846

 A synthetic solution:

Mongolian SL 2000 Math Olympiad, https://www.facebook.com/photo?fbid=4456586367743139&set=gm.1744931542378025

 

aophttps://artofproblemsolving.com/community/c6t48f6h2483365_amxcp__bnxdq_is_constant_projections_of_square_on_tangents,

 

Abdilkadir Altintas, Geometria Top, https://www.facebook.com/photo?fbid=3025600111102321&set=gm.1076995453070823

 

Problem Pedro Miranda, Training Geometry Olympiad, https://www.facebook.com/photo/?fbid=4446745348734828&set=gm.572767433983574

 

aops, https://artofproblemsolving.com/community/c4t48f4h2703493_find_the_angles_of_a_triangle

 

https://www.facebook.com/photo/?fbid=4380229928729538&set=gm.1200780940413283

 A solution (?)

equilaterals

 Years ago I published the attached problem, with synthetic solution

Problem, S.R. Peru Geometrico, https://www.facebook.com/photo/?fbid=10222065396297018&set=gm.3807081229404742

 

First problem of https://www.facebook.com/Matem%C3%A1tica-preuniversitaria-111349621225123/photos/pcb.135514875475264/135514668808618/

 A solution, out of scheduled training

Geometria Top, Gokham Aydin, https://www.facebook.com/photo/?fbid=3503645329711506&set=gm.864109817692722

 

Ahmet Cetin, Geometria Top, https://www.facebook.com/photo/?fbid=4356787147770274&set=gm.1053504675419901

 Completion of the proof can be seen at https://artofproblemsolving.com/community/c6t48f6h2683868_a_right_angled__triangle_and_bisector

ONM Costa Rica 2018, https://artofproblemsolving.com/community/c6t48f6h2684613_bf__cg_wanted_bd__ec_given_line__angle_bisector

 

aops, https://artofproblemsolving.com/community/c6t48f6h2669101_short_geo_problem

 

IGO 2014, aops, Morteza Saghafian, https://artofproblemsolving.com/community/c6t48f6h1677987_equal_angles_when_ltc__lta__90o

 

Training Geometry Olimpiad, Problem 971 by Biro Istvan

 

Training Geometry Olympiad, Te Vie

 An easy solution

aops, https://artofproblemsolving.com/community/c4t48f4h2673256_three_squares

 

Portugal 2021, aops

 

Geometria top, Problem 16/09/2021, https://www.facebook.com/photo/?fbid=10223936883428665&set=gm.1047502702686765

 

Torricelli - Fermat application, https://www.facebook.com/photo/?fbid=1264048620734007&set=gm.1203976553447767

 

easy but ... very easy, https://artofproblemsolving.com/community/c6t48f6h2668542_apparantly_easy_but

 

2021 Saudi Arabia JBMO Test, https://artofproblemsolving.com/community/c6t48f6h2664592_bckm_if_cmck_and_ltcbm__2_ltabm_and_k_lies_on_median_bm

 

aops, https://artofproblemsolving.com/community/c4t48f4h2665388_ma_bisects_ltkml__kc__ac_lbab_2012_arg_regional_cpr_32

 

Stanley Rabinowitz, Romantics of Geometry, 8804

 

aops, https://artofproblemsolving.com/community/c6t48f6h2664576_geometria