# Geometry - math word problems

1. Semicircle In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
2. The bridge Across the circle lakepasses through its center bridge over the lake. At three different locations on the lake shore are three fishermen A, B, C. Which of fishermen see the bridge under the largest angle?
3. See harmonics It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases.
4. Center of gravity The mass points are distributed in space as follows - specify by coordinates and weight. Find the center of gravity of the mass points system: A1 [1; -20; 3] m1 = 46 kg A2 [-20; 2; 9] m2 = 81 kg A3
5. Square side Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
6. Parabola Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)
7. Circumferential angle Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 2:2:9. Determine the size of the angles of the triangle ΔABC.
8. Lie/do not lie The function is given by the rule f(x) = 8x+16. Determine whether point D[-1; 8] lies on this function. Solve graphically or numerically and give reasons for the your answer.
9. Circles How many different circles is determined by 9 points at the plane, if 6 of them lie in a straight line?
10. Linear independence Determine if vectors u=(-4; -5) and v=(20; 25) are linear Linear dependent.
11. Unit vector 2D Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
12. Similarity coefficient The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of ​​the larger triangle.
13. Mine What is temperature in the mine at a depth of 1160 m, where at depth 9 m is 11°C and every 100 m, the temperature increases by 0.7°C?
14. Vector Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
15. Hexagon There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
16. XY triangle Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
17. Geodesist Triangle shaped field (triangle ABC) has side AB = 129 m. path XY is parallel to the side AB which divided triangle ABC into two parts with same area. What will be the length of the path XY? Help please geodesist ...
18. Boat A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight?
19. Vectors For vector w is true: w = 2u-5v. Determine coordinates of vector w if u=(3, -1), v=(12, -10)
20. Railways Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.

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