# Geometry - math word problems

1. Circle Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
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. Triangle KLB It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area o
4. Distance Calculate distance between two points X[18; 19] and W[20; 3].
5. Circumscribing Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
6. Trapezoid MO-5-Z8 ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid A
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. Segments Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
9. Right triangle Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
10. 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?
11. Perpendicular What is the slope of the perpendicular bisector of line segment AB if A[9,9] and B[9,-2]?
12. Lines In how many points will intersect 14 different lines, where no two are parallel?
13. Perpendicular Determine the slope of the line perpendicular to the line p: y = -x +4.
14. Line Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
15. Circle Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
16. 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].
17. Semicircle In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
18. Center Calculate the coordinates of the circle center: ?
19. 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?
20. Sun rays If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei

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