# Geometry - math word problems

#### Number of problems found: 324

- Dodecagon

Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees. - Divide in ratio

Line segment AB 12 cm long divide in a ratio of 5: 3. How long are the individual parts? - Cutting cone

A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm. - Interior angles

In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles. - My father

My father cut 78 slats on the fence. The shortest of them was 97 cm long, the longer one was 102 cm long. What was the total length of the slats in cm? - The triangles

The triangles KLM and ABC are given, which are similar to each other. Calculate the lengths of the remaining sides of the triangle KLM, if the lengths of the sides are a = 7 b = 5.6 c = 4.9 k = 5 - Coordinates hexagon

The regular hexagon ABCDEF is given. Point A has coordinates [1; 3] and point D has coordinates [4; 7]. Calculate the sum of the coordinates of the center of its described circle. - Lookout tower

Calculate the height of a lookout tower forming a shadow of 36 m if at the same time a column 2.5 m high has a shadow of 1.5 m. - Similarity of two triangles

The KLM triangle has a side length of k = 6.3cm, l = 8.1cm, m = 11.1cm. The triangle XYZ has a side length of x = 8.4cm, y = 10.8cm, z = 14.8cm. Are triangle KLM and XYZ similar? (write 0 if not, if yes, find and write the coefficient of a similarity) - Clock hands

Calculate the internal angles of a triangle whose vertices lie on the clock's 2, 6 and 11 hours. - Outside tangents

Calculate the length of the line segment S_{1}S_{2}if the circles k_{1}(S_{1}, 8cm) and k2 (S_{2},4cm) touch the outside. - Decide 2

Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line - Chord BC

A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]? - Vector perpendicular

Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1) - Vector equation

Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent - Angle of the body diagonals

Using vector dot product calculate the angle of the body diagonals of the cube. - Coordinates of a centroind

Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians). - Suppose

Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not? - A cell tower

A cell tower is located at coordinates (-5, -7) and has a circular range of 12 units. If Mr. XYZ is located at coordinates (4,5), will he be able to get a signal? - Two chords

In a circle with radius r = 26 cm two parallel chords are drawn. One chord has a length t1 = 48 cm and the second has a length t2 = 20 cm, with the center lying between them. Calculate the distance of two chords.

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