MathDB

2017.1

Part of Swiss NMO - geometry

Problems(1)

AD = AO wanted, 2 circles and angle bisector related

Source: Switzerland - Swiss ΜΟ 2017 p1

7/14/2020
Let AA and BB be points on the circle kk with center OO, so that AB>AOAB> AO. Let CC be the intersection of the bisectors of ∠OAB\angle OAB and kk, different from AA. Let DD be the intersection of the straight line ABAB with the circumcircle of the triangle OBCOBC, different from BB. Show that AD=AOAD = AO .
geometryangle bisectorcirclesequal segments