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2010014007

Level:

The picture shows first three patterns formed by green dots. The numbers of dots in patterns correspond to terms of a geometric sequence. To which term corresponds a pattern that will use

192

dots?

Seventh

Eighth

Tenth

Nineth

2110014002

Level:

In one of the pictures given below is not a graph of a part of a geometric sequence. Choose this graph.

2110014001

Level:

In one of the pictures given below is not a graph of a part of a geometric sequence. Choose this graph.

2010012810

Level:

In the triangle

K L M

k = 10 cm

l = 8 cm

m = 12 cm

. Point

N

is the foot of the altitude from the vertex

K

(See the picture.) What is the radius of the circumcircle of the triangle

K L N

6 cm

5 cm

7 cm

8 cm

2010012808

Level:

A regular nonagon

A B C D E F G H I

is inscribed in a circle. Calculate the measures of all interior angles of the quadrilateral

B D G I

. (See the picture.)

α = 100^{\circ}; β = 80^{\circ}; γ = 80^{\circ}; δ = 100^{\circ}

α = 110^{\circ}; β = 80^{\circ}; γ = 80^{\circ}; δ = 90^{\circ}

α = 110^{\circ}; β = 70^{\circ}; γ = 70^{\circ}; δ = 110^{\circ}

α = 120^{\circ}; β = 80^{\circ}; γ = 80^{\circ}; δ = 120^{\circ}

2010012807

Level:

A regular dodecagon

A B C D E F G H I J K L

is inscribed in a circle. Find the measures of all interior angles of the quadrilateral

B F I L

. (See the picture.)

α = 90^{\circ}; β = 75^{\circ}; γ = 90^{\circ}; δ = 105^{\circ}

α = 90^{\circ}; β = 60^{\circ}; γ = 80^{\circ}; δ = 130^{\circ}

α = 80^{\circ}; β = 75^{\circ}; γ = 90^{\circ}; δ = 115^{\circ}

α = 90^{\circ}; β = 105^{\circ}; γ = 90^{\circ}; δ = 105^{\circ}

2010012806

Level:

Points

A

and

B

divide the circle

k

into two arcs whose lengths are in the ratio

3 : 12

. Point

C

is an interior point of the longer arc. What is the degree measure of the angle

A C B

36^{\circ}

72^{\circ}

24^{\circ}

45^{\circ}

2010012805

Level:

Give the measure of the angle between two line segments: the first connecting numbers

6

and

11

, the second connecting numbers

8

and

2

on a clock face. (See the picture.)

75^{\circ}

30^{\circ}

60^{\circ}

45^{\circ}

2010012804

Level:

Give the measure of the angle contained by two line segments with the endpoints at the numbers

6

5

and

6

9

on a clock face. (See the picture.)

120^{\circ}

135^{\circ}

100^{\circ}

60^{\circ}

2010012803

Level:

What is the measure of the angle contained by two line segments: the first joining numbers

6

and

10

, and the second joining numbers

6

and

4

, on a clock face? (See the picture.)

90^{\circ}

60^{\circ}

85^{\circ}

95^{\circ}

A

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