MathDB

7

Part of 2015 Tuymaada Olympiad

Problems(2)

Some another geometry

Source: Tuymaada 2015, Day 2, Problem 7, Senior League

7/10/2017
In △ABC\triangle ABC points M,OM,O are midpoint of ABAB and circumcenter. It is true, that OM=R−rOM=R-r. Bisector of external ∠A\angle A intersect BCBC at DD and bisector of external ∠C\angle C intersect ABAB at EE. Find possible values of ∠CED\angle CED
D. Shiryaev
geometrycircumcircle
Incircle and bisector

Source: Tuymaada 2015, Day 1, Problem 7, Junior League

7/10/2017
CLCL is bisector of ∠C\angle C of ABCABC and intersect circumcircle at KK. II - incenter of ABCABC. IL=LKIL=LK. Prove, that CI=IKCI=IK
D. Shiryaev
geometryincenter