MathDB

3

Part of 2014 Oral Moscow Geometry Olympiad

Problems(2)

convex pentagon in which each diagonal is equal to a side?

Source: 2014 Oral Moscow Geometry Olympiad grades 8-9 p3

8/9/2019
Is there a convex pentagon in which each diagonal is equal to a side?
geometryconvexpentagondiagonal
2 lines concurrent with circumcircle, angle bisectors, circumcircles related

Source: 2014 Oral Moscow Geometry Olympiad grades 10-11 p3

8/9/2019
The bisectors AA1AA_1 and CC1CC_1 of triangle ABCABC intersect at point II. The circumscribed circles of triangles AIC1AIC_1 and CIA1CIA_1 intersect the arcs ACAC and BCBC (not containing points BB and AA respectively) of the circumscribed circle of triangle ABCABC at points C2C_2 and A2A_2, respectively. Prove that lines A1A2A_1A_2 and C1C2C_1C_2 intersect on the circumscribed circle of triangle ABCABC.
geometrycircumcircleangle bisectorconcurrencyconcurrent