1003076805
Level:
A
If two interior angles of a triangle \( ABC \) have measures of \( 60^{\circ} \), then the triangle \( ABC \) is an/a:
equilateral triangle
isosceles triangle
right-angled triangle
obtuse triangle
Triangles
1003076806
Level:
A
Choose the false statement:
In a triangle the side opposite the smallest interior angle is the longest side of a triangle.
The sum of the interior angles of a triangle is \( 180^{\circ} \).
There is at most one obtuse interior angle in a triangle.
In a triangle the sum of any two sides is greater than the third side.
1003076807
Level:
A
The sum of all interior angles of an isosceles triangle with a right angle opposite the base is:
\( 180^{\circ} \)
\( 90^{\circ} \)
\( 60^{\circ} \)
\( 30^{\circ} \)
1003076810
Level:
A
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?
\( 5:6:7 \)
\( 4:5:6 \)
\( 2:3:4 \)
\( 3:4:5 \)
1103021702
Level:
A
Given the triangle \( ABC \) (see the picture), where \( \alpha:\beta=5:7 \) and the angle \( \gamma \) is by \( 42^{\circ} \) smaller than the angle \( \omega \), calculate the measure of \( \gamma \).
\( 108^{\circ} \)
\( 42^{\circ} \)
\( 30^{\circ} \)
\( 60^{\circ} \)
1103021704
Level:
A
Decide according to the diagram, which of the line segments \( a \), \( b \), \( c \), \( d \), \( e \) is the longest.
\( d \)
\( a \)
\( b \)
\( c \)
1103021706
Level:
A
In the triangle \( ABC \), \( \alpha=80^{\circ} \) and \( \beta=70^{\circ} \) (see the picture). Determine the measure of the angle between the altitude to the side \( AB \) and the altitude to the side \( BC \).
\( 70^{\circ} \)
\( 120^{\circ} \)
\( 30^{\circ} \)
\( 60^{\circ} \)
1103021708
Level:
A
What is the measure of the angle \( \alpha \)? (See the picture.)
\( 7^{\circ} \)
\( 76^{\circ} \)
\( 83^{\circ} \)
\( 16^{\circ} \)
1103021709
Level:
A
The picture shows an isosceles triangle \( ABC \) with the base \( AB \). Calculate the measure of the angle \( \alpha \).
\( 31^{\circ} \)
\( 62^{\circ} \)
\( 118^{\circ} \)
\( 59^{\circ} \)
1103076811
Level:
A
A circle is inscribed into an isosceles triangle. The base of the triangle is \( 4\,\mathrm{cm} \) long and the length of the altitude to the base is \( 10\,\mathrm{cm} \). Calculate the radius of the circle.
\( 1.64\,\mathrm{cm} \)
\( 0.82\,\mathrm{cm} \)
\( 0.20\,\mathrm{cm} \)
\( 0.12\,\mathrm{cm} \)