2000003201
Level:
A
There is a triangle ABC in the picture. Choose the correct statement.
The triangle is isosceles.
The triangle is equilateral.
The triangle is right-angled.
The triangle is obtuse.
Triangles
2000003202
Level:
A
An isosceles triangle \(ABC\) is given in the picture. What are the measures of its interior angles?
\( \alpha=27^{\circ};~\beta=27^{\circ};~\gamma=126^{\circ}\)
\( \alpha=54^{\circ};~\beta=54^{\circ};~\gamma=72^{\circ}\)
\( \alpha=63^{\circ};~\beta=63^{\circ};~\gamma=153^{\circ}\)
\( \alpha=126^{\circ};~\beta=27^{\circ};~\gamma=27^{\circ}\)
2000003205
Level:
A
There is an equilateral triangle \(ABC\) in the picture. Choose the correct statement.
The triangle KBC is acute-angled.
The triangle KBC is right-angled.
The triangle KBC is obtuse-angled.
The triangle KBC is isosceles.
2000005506
Level:
A
The picture shows a triangle \(ABC\) with a central transversal \(EF\). The area of the trapezoid \(ABFE\) is \(24\,\mathrm{cm}^2\). What is the area of the triangle \(EFC\)?
\(8\,\mathrm{cm}^2\)
\(4\,\mathrm{cm}^2\)
\(16\,\mathrm{cm}^2\)
\(12\,\mathrm{cm}^2\)
2010012810
Level:
A
In the triangle \( KLM \), \( k=10\,\mathrm{cm} \), \( l=8\,\mathrm{cm} \), \( m=12\,\mathrm{cm} \). Point \( N \) is the foot of the altitude from the vertex \( K \) (See the picture.) What is the radius of the circumcircle of the triangle \( KLN \)?
\( 6\,\mathrm{cm} \)
\( 5\,\mathrm{cm} \)
\( 7\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)
2010015201
Level:
A
Interior angles of a triangle \( ABC \) are in the ratio \( \alpha:\beta:\gamma=3:5:7 \). Calculate the measures of these angles.
\( \alpha=36^{\circ};\ \beta=60^{\circ};\ \gamma=84^{\circ} \)
\( \alpha=30^{\circ};\ \beta=50^{\circ};\ \gamma=70^{\circ} \)
\( \alpha=16.5^{\circ};\ \beta=30^{\circ};\ \gamma=133.5^{\circ} \)
\( \alpha=84^{\circ};\ \beta=60^{\circ};\ \gamma=36^{\circ} \)
2010015205
Level:
A
The measures of two interior angles of a triangle are \( 61^{\circ}20' \) and \( 28^{\circ} \). What is the measure of the third interior angle?
\( 90^{\circ}40' \)
\( 33^{\circ}20' \)
\( 145^{\circ}20' \)
\( 147^{\circ}40' \)
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 \( AB \).
\( 80^{\circ} \)
\(30^{\circ}\)
\(70^{\circ}\)
\(100^{\circ}\)
9000045705
Level:
A
Find the formula for the radius \(r\)
of the circle circumscribed to the right triangle.
\(r = \frac{a}
{2\cdot \sin \alpha } \)
\(r = \frac{2a}
{\sin \alpha } \)
\(r = \frac{a}
{\sin 2\alpha } \)
\(r = \frac{a}
{\sin \alpha } \)
9000121701
Level:
A
Consider a triangle \(ABC\) with
sides of the lengths \(3\, \mathrm{cm}\),
\(4\, \mathrm{cm}\) and
\(4\, \mathrm{cm}\). Identify the type
of the triangle \(ABC\).
isosceles
equilateral
right
obtuse