Circles

9000045706

Level: 
B
Given a regular pentagon with the side \(a\), find the radius \(r\) of the circle circumscribed to this pentagon.
\(r = \frac{a} {2\cdot \cos 54^{\circ }}\)
\(r = \frac{2a} {\cos 72^{\circ }}\)
\(r = \frac{2a} {\cos 54^{\circ }}\)
\(r = \frac{a} {2\cdot \cos 72^{\circ }}\)

9000045707

Level: 
B
Given a regular pentagon with the side \(a\), find the radius \(\rho \) of the circle inscribed to this pentagon.
\(\rho = \frac{a} {2} \cdot \mathop{\mathrm{tg}}\nolimits 54^{\circ }\)
\(\rho = \frac{2a} {\mathop{\mathrm{tg}}\nolimits 54^{\circ }}\)
\(\rho = \frac{a} {2\cdot \mathop{\mathrm{tg}}\nolimits 54^{\circ }}\)
\(\rho = 2a\cdot \mathop{\mathrm{tg}}\nolimits 54^{\circ }\)

9000045708

Level: 
B
Given a regular hexagon with the side \(a\), find the radius \(\rho \) of the circle inscribed to this hexagon.
\(\rho = \frac{a} {2\cdot \mathop{\mathrm{tg}}\nolimits 30^{\circ }}\)
\(\rho = 2a\cdot \mathop{\mathrm{tg}}\nolimits 30^{\circ }\)
\(\rho = \frac{2a} {\mathop{\mathrm{tg}}\nolimits 30^{\circ }}\)
\(\rho = 2a\cdot \mathop{\mathrm{tg}}\nolimits 60^{\circ }\)

9000036105

Level: 
C
The side \(b\) in the triangle \(ABC\) is \(17\, \mathrm{cm}\) and the angle \(\beta \) is \(58^{\circ }\). Find the radius of the circle circumscribed to this triangle and round your answer to the nearest centimeters.
\(10\, \mathrm{cm}\)
\(8\, \mathrm{cm}\)
\(9\, \mathrm{cm}\)
\(11\, \mathrm{cm}\)

9000035002

Level: 
B
A line segment of the length \(40\, \mathrm{cm}\) joins two points on a circle. The radius of the circle is \(30\, \mathrm{cm}\). An angle has the vertex in the center of the circle and the arms on the ends of the line segment. Find the size of this angle and round the result to the nearest degrees and minutes.
\(83^{\circ }37'\)
\(97^{\circ }10'\)
\(41^{\circ }48'\)
\(96^{\circ }22'\)