A

2010015607

Level: 
A
The rectangular box \( ABCDA'B'C'D' \) has edges of lengths \( |AB|=5\,\mathrm{cm} \) and \( |BC|=6\,\mathrm{cm} \). The distance between the center of the top face \(A'B'C'D'\) and the center of the bottom face \(ABCD\) is \(12\,\mathrm{cm}\). Find the length of the diagonal \(DC'\).
\( 13\,\mathrm{cm} \)
\( 6\sqrt5 \,\mathrm{cm} \)
\( \sqrt{119}\,\mathrm{cm} \)
\(6 \sqrt{3}\,\mathrm{cm} \)

2010015606

Level: 
A
The rectangular box \( ABCDA'B'C'D' \) has edges of lengths \( |AB|=4\sqrt3\,\mathrm{cm} \) and \( |BC|=8\,\mathrm{cm} \). The point \(S\) is the center of the lateral face \(ADD'A'\) (see the picture) and the length of the line segment \(B'S\) is \(10\,\mathrm{cm}\). Find the distance between the points \(A\) and \(A'\).
\( 12\,\mathrm{cm} \)
\( 6\,\mathrm{cm} \)
\( \sqrt{164}\,\mathrm{cm} \)
\( \sqrt{272}\,\mathrm{cm} \)

2010015605

Level: 
A
The rectangular box \( ABCDA'B'C'D' \) has edges of lengths \( |AB|=6\,\mathrm{cm} \) and \( |BC|=8\,\mathrm{cm} \). The point \(S\) is the center of the base \(ABCD\) (see the picture) and the length of the line segment \(A'S\) is \(13\,\mathrm{cm}\). Find the distance between the points \(A\) and \(A'\).
\( 12\,\mathrm{cm} \)
\( \sqrt{194}\,\mathrm{cm} \)
\( \sqrt{69}\,\mathrm{cm} \)
\( 4\sqrt{10}\,\mathrm{cm} \)

2010015208

Level: 
A
In the triangle \( ABC \), \( \alpha=80^{\circ} \) and \( \gamma=30^{\circ} \) (see the picture). Determine the measure of the angle between the altitude to the side \( AC \) and the altitude to the side \( AB \).
\( 80^{\circ} \)
\(30^{\circ}\)
\(70^{\circ}\)
\(100^{\circ}\)