High school geometry

Answer all the questions below and press submit to see how many you got right.

id: 7931
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A quadrilateral ABCD is called cyclic if all of its points lie on a circle. Choose all statements that are true for a cyclic quadrilateral.

  • Opposite sides have the same lengths.
    ABCD is a rhombus.
    Opposite angles add up to $180^{\circ}.$
    The two diagonals of ABCD are perpendicular.
id: 7924
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We look at a triangle with corners A,B and C. We call the sides opposite of A,B and C a, b and c and the midpoints of a,b,c D,E and F. Select all the statements that are true.

  • AD, BE and CF intersect in a point Z that cuts these line segments in the ratio 2:1.
    If AD and BE cross in X, AD and CF in Y and BE and CF in Z the XYZ is a right triangle.
    If AD, BE and CF intersect in a point Z, ABC is a right triangle.
    AD, BE and CF intersect in a point Z that cuts these line segments in the ratio 1:1.
id: 7915
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A line PQ and a line XY cross each other in a point O. Choose all statements that are true if the line PX is parallel to the line QY.

  • The ratio of the lengths of the line segments OY and OX is equal to the ratio of the lengths of the line segments OQ and OP.
    The ratio of the lengths of the line segments QY and PX is equal to the ratio of the lengths of the line segments OY and OX.
    The ratio of the lengths of the line segments QY and PX is equal to the ratio of the lengths of the line segments OQ and OP.
    The ratio of the lengths of the line segments OY and OX is equal to the ratio of the lengths of the line segments PX and QY.