# Geometry - math word problems

- 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. - 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°? - 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 - Vector

Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2). - Segment

Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5]. - Circumscribing

Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm. - Slope

What is the slope of the line defined by the equation -2x +3y = -1 ? - 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? - OK circle

Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17. - Center

Calculate the coordinates of the circle center: ? - 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 - Perpendicular

What is the slope of the perpendicular bisector of line segment AB if A[9,9] and B[9,-2]? - Segments

Which of the pairs of numbers on the number line encloses the longest segment: ? - 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? - Distance

Calculate distance between two points X[18; 19] and W[20; 3]. - Circle

Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ? - Perpendicular

Determine the slope of the line perpendicular to the line p: y = -x +4. - Slope

What is the slope of a line with an inclination 6.06 rad? - Line

Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p? - 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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