1003023201
Level:
A
Subtract the angles \( \alpha=1285^{\circ} 35' \), \( \beta= 985^{\circ}59' \) and round the result to the nearest degree.
\( 300^{\circ} \)
\( 299^{\circ} \)
\( 301^{\circ} \)
\( 298^{\circ} \)
A
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.
\( 1.64\,\mathrm{cm} \)
\( 0.82\,\mathrm{cm} \)
\( 0.20\,\mathrm{cm} \)
\( 0.12\,\mathrm{cm} \)
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?
\( 5:6:7 \)
\( 4:5:6 \)
\( 2:3:4 \)
\( 3:4:5 \)
1003076807
Level:
A
The sum of all interior angles of an isosceles triangle with a right angle opposite the base is:
\( 180^{\circ} \)
\( 90^{\circ} \)
\( 60^{\circ} \)
\( 30^{\circ} \)
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.
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
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?
\( 123^{\circ}40' \)
\( 56^{\circ}20' \)
\( 5^{\circ}40' \)
\( 124^{\circ}40' \)
1003076803
Level:
A
Choose the false statement:
There exists a right-angled equilateral triangle.
There exists an acute isosceles triangle.
There exists an acute equilateral triangle.
There exists an obtuse isosceles triangle.
1003076802
Level:
A
If the orthocenter of a triangle lies outside the triangle, then it is an/a:
obtuse triangle
right-angled triangle
acute triangle
equilateral triangle
1003076801
Level:
A
\( ABC \) is a triangle with sides \( a \), \( b \), \( c \). Let \( a\leq b\leq c \). Two of its interior angles have measures of \( 70^{\circ} \) and \( 50^{\circ} \). Which of the following statements about the triangle \( ABC \) is true?
The third interior angle is opposite the side \( b \).
The angle of the measure \( 70^{\circ} \) lies opposite the side \( a \).
The angle of the measure \( 50^{\circ} \) lies opposite the side \( b \).
The third interior angle is opposite the side \( c \).