MathDB

5

Part of 2011 Oral Moscow Geometry Olympiad

Problems(2)

<BDC when AC\perp BD, <BCA = 10^o,<BDA = 20^o, <BAC = 40^o

Source: 2011 Oral Moscow Geometry Olympiad grades 10-11 p5

4/7/2020
In a convex quadrilateral ABCD,AC⊥BD,∠BCA=10o,∠BDA=20o,∠BAC=40oABCD, AC\perp BD, \angle BCA = 10^o,\angle BDA = 20^o, \angle BAC = 40^o. Find ∠BDC\angle BDC.
Angle Chasinganglesperpendiculargeometry
collinear wanted, circumcircles related to an isosceles

Source: 2011 Oral Moscow Geometry Olympiad grades 8-9 p5

4/17/2020
Let AA1AA _1 and BB1BB_1 be the altitudes of an isosceles acute-angled triangle ABC,MABC, M the midpoint of ABAB. The circles circumscribed around the triangles AMA1AMA_1 and BMB1BMB_1 intersect the lines ACAC and BCBC at points KK and LL, respectively. Prove that K,MK, M, and LL lie on the same line.
geometrycircumcirclecollinearisosceles