# Equation + right triangle - math problems

1. Circle and square An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
2. An equilateral An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
3. Angled cyclist turn The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?
4. Three parallels The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
5. Land boundary The land has the shape of a right triangle. The hypotenuse has a length of 30m. The circumference of the land is 72 meters. What is the length of the remaining sides of the land boundary?
6. Sides of right angled triangle One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
7. The hemisphere The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
8. Secret treasure Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
9. Medians in right triangle It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?
10. Faces diagonals If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.3, y=1, z=1.2
11. Two chords Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
12. Touch x-axis Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
13. RT sides Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
14. Find parameters Find parameters of the circle in the plane - coordinates of center and radius: ?
15. Rectangle There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
16. Rectangular triangle The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
17. Diamond diagonals Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
18. Diagonals of a rhombus 2 One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
19. On line On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
20. Distance problem 2 A=(x,2x) B=(2x,1) Distance AB=√2, find value of x

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