# Geometry - math word problems

1. Hyperbola Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].
2. Two angles The triangles ABC and A'B'C 'are similar. In the ABC triangle, the two angles are 25° and 65°. Explain why in the triangle A'B'C 'is the sum of two angles of 90 degrees.
3. Ellipse Ellipse is expressed by equation 9x2 + 25y2 - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
4. Area of iso-trap Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other.
5. Find the 3 Find the distance and mid-point between A(1,2) and B(5,5).
6. Same area There is a given triangle. Construct a square of the same area.
7. Hypotenuse - RT A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
8. A boy A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff. Miro stands under a tree and watching its shadow and shadow of the tree. Miro is 180 cm tall and its shade is 1.5 m long. The shadow of the tree is three times as long as Miro's shadow. How tall is the tree in meters?
10. Curve and line The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
11. Three points 2 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
12. Line segment The 4 cm long line segment is enlarged in the ratio of 5/2. How many centimeters will measure the new line segment?
13. Coordinate axes Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
14. Trapezoid - intersection of diagonals In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.
15. Inscribed circle Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
16. Two forces The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
17. Sphere equation Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
18. Equation of circle 2 Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
19. Tangent What distance is the tangent t of the circle (S, 4 cm) and the chord of this circle, which is 6 cm long and parallel to the tangent t?
20. Rectangle 39 Find the perimeter and area of the rectangular with vertices (-1, 4), (0,4), (0, -1), and (-4, 4)

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...