Subcontests
(1)19th Cabri Clubs 2007, round 1, level 1, 3 problems, Argentinian geo contest
level 1
p1. Given an acute triangle ABC, point D in BC and point E in AC are marked, so that ∠AEB=∠ADB=90o. The bisectors of the angles ∠CAD and ∠CBE intersect at F. Find the angle ∠AFB.
p2. [color=#f00](figure missing) Let ABC be an equilateral triangle with side 2 and let M,N and P be the midpoints of AB, BC and CA respectively. Draw the three circles of radius 1 centered at A,B, and C.
a) Calculate the area of the shaded region in figure A.
b) The circle that passes through M,N and P. is drawn. Calculate the area of the shaded region in figure B.
p3. Let ABC be a triangle. Let D be the midpoint of AB and let E be a point on segment BC such that BE=2EC. Knowing that ∠BAE=∠ADC , find the angle ∠BAC. 19th Cabri Clubs 2007, round 1, level 2, 3 problems, Argentinian geo contest
level 2
p4. Let ABC be a triangle with side AB less than side AC. D is marked on the side AC, such that AD=AB. Knowing that ∠ABC−∠ACB=48o, calculate the measure of the angle ∠DBC.
p5. Let ABC be a right triangle at A. D,E, and F are marked on side BC so that AD is perpendicular to BC, AE is the bisector of ∠BAC, and F is the midpoint of BC. Prove that AE is a bisector of ∠DAF.
p6. Let ABCD be a parallelogram and E a point on side BC. The line AE, which intersects the extension of the side DC at F, and the diagonal BD, which intersects the segment AE at G. Knowing that AG=6 and GE=4, find the length of the drawn segment EF.