# Geometry - math word problems

1. Triangle
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
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
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
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
5. Segment
Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5].
6. Circumscribing
Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
7. Slope
What is the slope of the line defined by the equation -2x +3y = -1 ?
8. Climb
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
Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.
10. Center
Calculate the coordinates of the circle center: ?
11. Circle
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
What is the slope of the perpendicular bisector of line segment AB if A[9,9] and B[9,-2]?
13. Segments
Which of the pairs of numbers on the number line encloses the longest segment: ?
14. Cone
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
Calculate distance between two points X[18; 19] and W[20; 3].
16. Circle
Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
17. Perpendicular
Determine the slope of the line perpendicular to the line p: y = -x +4.
18. Slope
What is the slope of a line with an inclination 6.06 rad?
19. Line
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
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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