Let ABC be an acute triangle with AB=AC. The angle bisector of ∠BAC intersects with BC at a point D. BE,CF are the altitudes of the triangle and Ap1,Ap2 are the isodynamic points of triangle ABC.Let the A-median of ABC intersect EF at T. Show that the line connecting T with the nine-point center of ABC is perpendicular to BC if and only if ∠Ap1DAp2=90∘. geometryangle bisectorapollonius circleNine point center