Lines and planes: intersecting, perpendicular, parallel

1003030302

Level: 
A
Let \( p \) be a line and \( k \) be a circle with the centre \( S \) and the radius of \( 3\,\mathrm{cm} \). Given the distance of \( p \) and \( S \) is \( 2.8\,\mathrm{cm} \), the line \( p \) is:
a secant of the circle \( k \)
a tangent of the circle \( k \)
an outer line of the circle \( k \)
a chord of the circle \( k \)

1003030303

Level: 
A
Let \( k_1 \) and \( k_2 \) be circles with the centres \( S_1\), \( S_2 \), and the radii of lengths \( 5\,\mathrm{cm} \) and \( 1\,\mathrm{cm} \) consecutively. Given \( |S_1 S_2|=3\,\mathrm{cm} \), what is the mutual position of these circles?
The circle \( k_2 \) lies inside the circle \( k_1 \).
The circle \( k_1 \) lies inside the circle \( k_2 \).
The circles \( k_1 \) and \( k_2 \) intersect.
The circles \( k_1 \) and \( k_2 \) are externally tangent.
The circles \( k_1 \) a \( k_2 \) are internally tangent.

1003030304

Level: 
A
Let \( k_1 \) and \( k_2 \) be circles with the centres \( S_1 \), \( S_2 \), and the radii of lengths \( 5\,\mathrm{cm} \) and \( 1\,\mathrm{cm} \) consecutively. Given \( |S_1 S_2 |=7\,\mathrm{cm} \), what is the mutual position of these circles?
The circle \( k_2 \) lies outside the circle \( k_1 \).
The circle \( k_2 \) lies inside the circle \( k_1 \).
The circles \( k_1 \) and \( k_2 \) intersect.
The circles \( k_1 \) and \( k_2 \) are externally tangent.
The circles \( k_1 \) and \( k_2 \) are internally tangent.

1003030305

Level: 
A
Let \( k_1 \) and \( k_2 \) be circles with the centres \( S_1 \), \( S_2 \), and the radii of lengths \( 5\,\mathrm{cm} \) and \( 1\,\mathrm{cm} \) consecutively. Given \( |S_1S_2|=6\,\mathrm{cm}\), what is the mutual position of these circles?
The circles \( k_1 \) and \( k_2 \) are externally tangent.
The circles \( k_1 \) and \( k_2 \) are internally tangent.
The circle \( k_1 \) lies inside the circle \( k_2 \).
The circle \( k_2 \) lies inside the circle \( k_1 \).

1003030306

Level: 
A
Let \( k_1 \) and \( k_2 \) be circles with the centres \( S_1 \), \( S_2 \), and the radii of lengths \( 5\,\mathrm{cm} \) and \( 1\,\mathrm{cm} \) consecutively. Given \( |S_1S_2|=4\,\mathrm{cm}\), what is the mutual position of these circles?
The circles \( k_1 \) and \( k_2 \) are internally tangent.
The circles \( k_1 \) and \( k_2 \) are externally tangent.
The circle \( k_1 \) lies inside the circle \( k_2 \).
The circle \( k_2 \) lies inside the circle \( k_1 \).

1003030307

Level: 
A
Let \( k_1 \) and \( k_2 \) be circles with the centres \( S_1 \), \( S_2 \), and the radii of lengths \( 5\,\mathrm{cm} \) and \( 1\,\mathrm{cm} \) consecutively. Given \( |S_1S_2|=5\,\mathrm{cm} \), what is the mutual position of these circles?
The circles \( k_1 \) and \( k_2 \) intersect.
The circles \( k_1 \) and \( k_2 \) are internally tangent.
The circles \( k_1 \) and \( k_2 \) are externally tangent.
The circle \( k_1 \) lies inside the circle \( k_2 \).
The circle \( k_2 \) lies inside the circle \( k_1 \).

1003030308

Level: 
A
Let \( k_1 \) and \( k_2 \) be circles with the centres \( S_1 \), \( S_2 \), and the radii of lengths \( 5\,\mathrm{cm} \) and \( 1\,\mathrm{cm} \) consecutively. Given \(S_1=S_2\), what is the mutual position of these circles?
The circles \( k_1 \) and \( k_2 \) are concentric.
The circles \( k_1 \) and \( k_2 \) intersect.
The circle \( k_1 \) lies inside the circle \( k_2 \).
The circle \( k_2 \) lies outside the circle \( k_1 \).
The circles \( k_1 \) and \( k_2 \) are internally tangent.