MathDB

36

Part of 1988 IMO Longlists

Problems(1)

Indian IMO LongList 1988 Geometry Problem

Source: IMO LongList 1988, India 1, Problem 36 of ILL

11/3/2005
i.) Let ABCABC be a triangle with AB=12AB = 12 and AC=16.AC = 16. Suppose MM is the midpoint of side BCBC and points EE and FF are chosen on sides ACAC and ABAB, respectively, and suppose that lines EFEF and AMAM intersect at G.G. If AE=2⋅AFAE = 2 \cdot AF then find the ratio EGGF \frac{EG}{GF} ii.) Let EE be a point external to a circle and suppose that two chords EABEAB and EDCEDC meet at angle of 40∘.40^{\circ}. If AB=BC=CDAB = BC = CD find the size of angle ACD.ACD.
geometryratioquadraticsalgebrageometry unsolved