Right triangle + circle - math problems

  1. Two circles
    intersect_circles Two circles with the same radius r = 1 are given. The center of the second circle lies on the circumference of the first. What is the area of a square inscribed in the intersection of given circles?
  2. Two chords
    tetivy 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.
  3. Touch x-axis
    touch_circle Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
  4. Company logo
    circle_square_insribed The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo?
  5. RT sides
    described_circle_right_triangle Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
  6. Annular area
    medzikrucie2 The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
  7. Ratio of sides
    described_circle2 Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
  8. The diagram 2
    cone The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
  9. Find parameters
    circle_axes_1 Find parameters of the circle in the plane - coordinates of center and radius: ?
  10. Distance problem
    linear_eq_3 A=(x, x) B=(1,4) Distance AB=√5, find x;
  11. Spherical cap 4
    spherical cap What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
  12. Circle annulus
    medzikruzie2 There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have?
  13. Circle described
    described_circle_right_triangle The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
  14. Waste
    doska_kruh How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?
  15. Inscribed rectangle
    rectangle_inside_circle What is the perimeter of a rectangle that is inscribed in a circle whose diameter is 5 dm long? Answer: 14 dm
  16. Quarter circle
    quarter_circle_1 What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
  17. RT - inscribed circle
    rt_incircle In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
  18. Pavement
    chodnik2 Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
  19. Hypotenuse - RT
    triangle_bac_1 A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
  20. Slant height
    cone_10 The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone

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