Euclidean theorems - examples

The altitude to the hypotenuse is the geometric mean of the two segments of the hypotenuse. Each leg of the right triangle is the mean proportional of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.
  1. Right Δ
    ruler Right triangle has length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
  2. Area of RT
    right_triangle_sepia Calculate the area of a right triangle which hypotenuse has length 20 and one hypotenuse segment has lenght 15.
  3. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  4. Tangents
    tangents To circle with a radius of 98 dm from the point A guided two tangents. The distance of both points of contact is 155 dm. Calculate the distance from point A and circle centre.
  5. Rectangle
    rectangle_ABCD In rectangle ABCD with sides |AB|=11, |AD|=12 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?.
  6. Rhombus and inscribed
    rhombus_2 Rhombus has side a = 72 cm, the radius of the inscribed circle is r = 10 cm. Calculate the length of its two diagonals.
  7. Rhombus
    rhomus_circle It is given a rhombus of side length a = 11 cm. Touch points of inscribed circle divided his sides into sections a1 = 6 cm and a2 = 5 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
  8. Without Euclid laws
    euclid_1 Right triangle ABC with right angle at the C has a=10 and hypotenuse c=27. Calculate the height h of this triangle without the use of Euclidean laws.
  9. Leg and height
    right_triangles Solve right triangle with height v = 9.6 m and shorter cathetus b = 17 m.
  10. Area of RT
    sandwich_rt In the right triangle has orthogonal projections of legs to the hypotenuse lengths 5 cm and 8 cm. Determine the area of ​​this triangle.
  11. Triangle ABC
    ABC Right triangle ABC with right angle at the C, |BC|=20, |AB|=35. Calculate the height of the triangle hAB to the side AB.
  12. Euclid1
    pravitko Right triangle has hypotenuse c = 15 cm. How large sections cuts height hc=7 cm on the hypotenuse c?
  13. Hypotenuse and height
    euklides In a right triangle is length of the hypotenuse c = 45 cm and height hc = 19 cm. Determine the length of both trangle legs.
  14. RT - hypotenuse and altitude
    pravy_trojuholnik Right triangle TWS has hypotenuse s=202 km and altitude to s is 99 km. How long are hypotenuse segments?
  15. Goat and circles
    equation_nonlinear What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g
  16. Euklid4
    euclid_2 Legs of a right triangle have dimensions 61 m and 39 m. Calculate the length of the hypotenuse and the height of this right triangle.
  17. Euclid2
    euclid In right triangle ABC with right angle at C is given side a=29 and height v=27. Calculate the perimeter of the triangle.
  18. Circle in rhombus
    circle_rhombus In the rhombus is inscribed circle. Contact points of touch divide the sides to parts of length 18 cm and 17 cm. Calculate the circle area.
  19. Euclid3
    euclid2 Calculate height and sides of the right triangle, if one leg is a = 50 km and section of hypotenuse adjacent to the second leg cb = 17 km.
  20. Circles
    pyt_theorem In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).

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