MathDB

3

Part of 2012 Greece JBMO TST

Problems(1)

2 equal circles, 1 symmetric point, 1 altitude, perpendicularity wanted

Source: Greece JBMO TST 2012 p3

4/29/2019
Let ABCABC be an acute triangle with AB<AC<BCAB<AC<BC, inscribed in circle c(O,R)c(O,R) (with center OO and radius RR). Let O1O_1 be the symmetric point of OO wrt ACAC. Circle c1(O1,R)c_1(O_1,R) intersects BCBC at ZZ. If the extension of the altitude ADAD intersects the cicrumscribed circle c(O,R)c(O,R) at point EE, prove that ECEC is perpendicular on AZAZ.
geometryperpendicularsymmetrycircumcirclecirclesaltitude