Geometry - math word problems

  1. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles.
  2. Similarity
    similar_triangle Are two right triangles similar to each other if the first one has a acute angle 70° and second one has acute angle 20°?
  3. Reverse Pythagorean theorem
    pytagors Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm
  4. Vector
    some_vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
  5. Segment
    segment_AB Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5].
  6. Circumscribing
    thales Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
  7. Slope
    slope What is the slope of the line defined by the equation -2x +3y = -1 ?
  8. Climb
    Mazda_RX7_1 On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went?
  9. OK circle
    circles2 Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.
  10. Center
    circle Calculate the coordinates of the circle center: ?
  11. Circle
    kruznica Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q. Write the equation of circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
  12. Perpendicular
    slopeplane What is the slope of the perpendicular bisector of line segment AB if A[9,9] and B[9,-2]?
  13. Segments
    abs Which of the pairs of numbers on the number line encloses the longest segment: ?
  14. Cone
    cones_1 If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
  15. Distance
    distance Calculate distance between two points X[18; 19] and W[20; 3].
  16. Circle
    circle_ag Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
  17. Perpendicular
    perpendicular Determine the slope of the line perpendicular to the line p: y = -x +4.
  18. Slope
    slope What is the slope of a line with an inclination 6.06 rad?
  19. Line
    img2 Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
  20. Center
    center_triangle In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].

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