1003076804
Level:
A
The measures of two interior angles of a triangle are \( 31^{\circ}20' \) and \( 25^{\circ} \). What is the measure of the third interior angle?
\( 123^{\circ}40' \)
\( 56^{\circ}20' \)
\( 5^{\circ}40' \)
\( 124^{\circ}40' \)
Triangles
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
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:
\( 180^{\circ} \)
\( 90^{\circ} \)
\( 60^{\circ} \)
\( 30^{\circ} \)
1103021512
Level:
A
In the triangle \( ABC \), \( a=10\,\mathrm{cm} \), \( b=8\,\mathrm{cm} \), \( c=12\,\mathrm{cm} \). Point \( D \) is the foot of the altitude from the vertex \( C \) (see the picture.) What is the radius of the circumcircle of the triangle \( DBC \)?
\( 5\,\mathrm{cm} \)
\( 4\,\mathrm{cm} \)
\( 6\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)
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 \( BC \).
\( 70^{\circ} \)
\( 120^{\circ} \)
\( 30^{\circ} \)
\( 60^{\circ} \)
1103077101
Level:
A
Derive the formula for calculating the perimeter of an equilateral triangle inscribed in a circle of radius \( r \).
\( 3\sqrt3 r \)
\( \sqrt3 r \)
\( 3 r \)
\( \frac{3\sqrt3 r}2 \)
1103077102
Level:
A
Derive the formula for calculating the perimeter of an equilateral triangle circumscribed about a circle of radius \( r \).
\( 6\sqrt3 r \)
\( 2\sqrt3 r \)
\( \frac{2r}{\sqrt3} \)
\( \frac{6r}{\sqrt3} \)