B

1103021611

Level: 
B
What is the length of the side of a regular pentagon circumscribed to a circle with radius of \( 9\,\mathrm{cm} \)? (See the picture.) Round the result to two decimal places.
\( 13.08\,\mathrm{cm} \)
\( 55.39\,\mathrm{cm} \)
\( 6.54\,\mathrm{cm} \)
\( 10.58\,\mathrm{cm} \)

1103021609

Level: 
B
Points \( A \), \( B \) and \( C \) lie on the circle \( k \). The line segment \( AC \) is the diameter of the circle and the lines \( AC \) and \( BC \) contain the angle of \( 60^{\circ} \). Calculate the length of \( AC \) if the length of \( BC \) is \( 10\,\mathrm{cm} \). (See the picture.)
\( 20\,\mathrm{cm} \)
\( 5\sqrt3\,\mathrm{cm} \)
\( 5\,\mathrm{cm} \)
\( 2\sqrt3\,\mathrm{cm} \)

1103021601

Level: 
B
The distance from the point \( V \) to the centre \( S \) of the circle \( k \) is \( 30\,\mathrm{cm} \). The radius of the circle is \( 15\,\mathrm{cm} \). From the point \( V \) two tangent lines to the circle \( k \) can be drawn. What is the measure of the angle between them? (See the picture.)
\( 60^{\circ} \)
\( 30^{\circ} \)
\( 90^{\circ} \)
\( 45^{\circ} \)

1003134706

Level: 
B
Find the second term and the common ratio of the geometric sequence \( \{a_n\}_{n=1}^{\infty} \), if: \[ \begin{aligned} a_2-a_1&=22, \\ a_3-a_2&=66. \end{aligned} \]
\( a_2=33 \), \( q=3 \)
\( a_2=11 \), \( q=3 \)
\( a_2=22 \), \( q=3 \)
\( a_2=33 \), \( q=2 \)
\( a_2=11 \), \( q=2 \)