MathDB

1

Part of 2002 Italy TST

Problems(2)

Find all possible values of AC

Source: Italy TST 2002

11/9/2010
Given that in a triangle ABCABC, AB=3AB=3, BC=4BC=4 and the midpoints of the altitudes of the triangle are collinear, find all possible values of the length of ACAC.
geometrycircumcirclegeometry unsolved
The circumcentre of triangle AED

Source: Italy TST 2002

11/9/2010
A scalene triangle ABCABC is inscribed in a circle Γ\Gamma. The bisector of angle AA meets BCBC at EE. Let MM be the midpoint of the arc BACBAC. The line MEME intersects Γ\Gamma again at DD. Show that the circumcentre of triangle AEDAED coincides with the intersection point of the tangent to Γ\Gamma at DD and the line BCBC.
geometrycircumcircleperpendicular bisectorgeometry unsolved