Question 1: The average of angles a and b of triangle ABC is equal to 55^o. What is the value of angle c?





60^o

65^o

70^o

75^o



Question 2: Triangle ABC has MN parallel to BC and AM/AB = 2/3. What is the ratio between the area of triangle AMN and the area of triangle ABC?


2/3

4/9

1/2

1/3



Question 3: What is the length of the segment BD in the figure below, if AD is 6cm?
Figure not drawn to scale


10cm

11cm

12cm

13cm




Question 4: What percentage of the area of the triangle below is shadowed? All triangles are equilateral.



60%

62.5%

65%

67.5%




Question 5: A circle of center O is inscribed in a right isosceles triangle, ABC as seen in the figure above. If side AC is tangent to the circle in point T and the radius of the circle is r, which of the following approximates best the length of the segment BT?



2.41r

2.5r

2.62r

2.75r



Question 6: In the picture given below, D is a point on the side BC of triangle ABC. Determine which of the following given assumptions are enough to prove that the ABD and ACD triangles are similar.



AD is the altitude of triangle ABC

triangle ABC is equilateral and AD is its median

triangle ABC is equilateral

∠ABC = ∠ACB



Question 7: In triangle ABC, MN is the mediator of segment B (MN ⊥ BC and BM = MC). If ∠BNM = α and ∠BAC = 2α, calculate the ratio between the lengths of segments MN and AC as a function of α.















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