Circles

9000121807

Level: 
A
In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon, the blue angle is the interior angle of the polygon. Suppose we consider a regular polygon with the central angle of \(40^{\circ}\), then find the measure of the interior angle of this polygon.
\(140^{\circ }\)
\(80^{\circ }\)
\(200^{\circ }\)
\(120^{\circ }\)

1003076810

Level: 
B
Interior angles of a triangle \( ABC \) are in the ratio \( 2:3:4 \). A circle is inscribed into the triangle \( ABC \). Points of tangency divide the circle into three arcs. What is the ratio of the lengths of these arcs?
\( 5:6:7 \)
\( 4:5:6 \)
\( 2:3:4 \)
\( 3:4:5 \)

1003077112

Level: 
B
The length of a circular arc with the central angle of \( 3.5 \) radians is \( 82\,\mathrm{cm} \). Calculate the radius of the corresponding circle. Round the result to two decimal places.
\( 23.43\,\mathrm{cm} \)
\( 287.00\,\mathrm{cm} \)
\( 1.59\,\mathrm{cm} \)
\( 4217.40\,\mathrm{cm} \)

1103077111

Level: 
B
A piece of land in the shape of a circular sector with central angle of \( 60^{\circ} \) needs to be fenced. We have used \( 10 \) metres of wire mesh on the curved part of the fence. How many conventional metres of mesh still have to be purchased? Round the result to the nearest metre.
\( 19\,\mathrm{m} \)
\( 10\,\mathrm{m} \)
\( 15\,\mathrm{m} \)
\( 25\,\mathrm{m} \)

1103077201

Level: 
B
The flower bed has the shape of a circle sector of radius \( 3\,\mathrm{m} \) with central angle \( 75^{\circ} \). Calculate the area of this flower bed. Round the result to two decimal places.
\( 5.89\,\mathrm{m}^2 \)
\( 1.96\,\mathrm{m}^2 \)
\( 11.78\,\mathrm{m}^2 \)
\( 9.34\,\mathrm{m}^2 \)

1103077203

Level: 
B
The tip of a minute hand is at distance of \( 15\,\mathrm{mm} \) from the clock centre. Calculate the length of the path the tip travels in \( 42 \) minutes. Round the result to two decimal places.
\( 65.97\,\mathrm{mm} \)
\( 94.20\,\mathrm{mm} \)
\( 35.27\,\mathrm{mm} \)
\( 72.12\,\mathrm{mm} \)

1103077204

Level: 
B
Given a circle, the length of the chord \( AB \) is \( 16\,\mathrm{cm} \) and the height \( v \) of the corresponding circular segment is \( 5\,\mathrm{cm} \) (see the picture). Calculate the area of the segment. Round the result to two decimal places.
\( 57.29\,\mathrm{cm}^2 \)
\( 55.12\,\mathrm{cm}^2 \)
\( 47.12\,\mathrm{cm}^2 \)
\( 63.12\,\mathrm{cm}^2 \)