MathDB

3

Part of 2012 Bundeswettbewerb Mathematik

Problems(2)

isosceles wanted, equilateral on square given

Source: Germany Federal - Bundeswettbewerb Mathematik 2012, round 1, p3

4/11/2020
An equilateral triangle DCEDCE is placed outside a square ABCDABCD. The center of this triangle is denoted as MM and the intersection of the straight line ACAC and BEBE with SS. Prove that the triangle CMSCMS is isosceles.
geometryisoscelesEquilateral TriangleEquilateral
CE=CB_1 wanted, diameter and touchpoint of incircle related

Source: Germany Federal - Bundeswettbewerb Mathematik 2012, round 2, p3

4/14/2020
The incircle of the triangle ABCABC touches the sides BC,CABC, CA and ABAB in points A1,B1A_1, B_1 and C1C_1 respectively. C1DC_1D is a diameter of the incircle. Finally, let EE be the intersection of the lines B1C1B_1C_1 and A1DA_1D. Prove that the segments CECE and CB1CB_1 have equal length.
geometryincircleequal segmentsdiameter