Thales' theorem - high school - practice problems
Number of problems found: 20
- Same area
There is a given triangle. Construct a square of the same area. - Circumscribing
Find the radius of the circumscribed circle to the right triangle with legs 6 cm and 3 cm. - Spectators 7562
The theater has the shape of a semicircle. A podium is the diameter of a semicircle. Spectators K, L, M, N, and O, sit around the perimeter. Who sees the podium at the greatest angle? - Circle tangent
It is given to a circle with the center S and a radius of 3.5 cm. The distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p. - Touch circle
Point A has a distance (A, k) = 10 cm from a circle k with radius r = 4 cm and center S. Calculate: a) the distance of point A from the point of contact T if the tangent to the circle is drawn from point A b) the distance of the contact point T from the l - Parallels and one secant
There are two different parallel lines, a, b, and line c, that intersect the two parallel lines. Draw a circle that touches all lines at the same time. - Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle? - Calculate 16223
The following elements are known in the right triangle ABC: a = 10 cm, height to side c h = 9.23 cm. Calculate o, R (radius of the inscribed circle), r (radius of the inscribed circle). - Circle described
The circle radius described in the right triangle with a 6 cm long leg is 5 cm. Calculate the circumference of this triangle. - Circumferential angle
Vertices of the triangle ΔABC lay on the circle and are divided into arcs in the ratio 7:8:7. Determine the size of the angles of the triangle ΔABC. - Construct 47633
Construct a square that has the area as a rhombus ABCD ak / AB / = 5cm, / AD / = 4cm and angle | DAB | = 30 ° - Inscribed triangle
To a circle is an inscribed triangle so that it is vertexes divide the circle into three arcs. The length of the arcs is in the ratio 2:3:7. Find the interior angles of a triangle. - Isosceles 7566
A right isosceles triangle is inscribed in the circle with r = 8 cm. Find triangle area S. How much percent does the triangle occupy the area of the circle? - Triangles 2157
Construct the vertices C of all triangles ABC, if given side AB, height vb on side b, and length of line tc on side c. Build all the solutions. Mark the vertices C1, C2,. .. - Rectangle
In a rectangle with sides, 8 and 9 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than any side of the rectangle? - Belongs 8412
Given a circle k(O; 2.5 cm), a line p: /Op/=4 cm, a point T: T belongs to p and at the same time /OT/=4.5 cm. We must find all the circles that will touch the circle k and the line p at point T. - Construct 11511
Construct the diamond ABCD so that its diagonal BD is 8 cm and the distance of apex B from the line AD is 5 cm. Specify all options - Triangle 73464
The given line is a BC length of 6 cm. Construct a triangle so that the BAC angle is 50° and the height to the side is 5.5 cm. Thank you very much. - Lunes of Hippocrates
Calculate the sum of the area of the so-called Hippocratic lunas, which were cut above the legs of a right triangle (a = 6cm, b = 8cm). Instructions: First, calculate the area of the semicircles above all sides of the ABC triangle. Compare the sum of the - MIT 1869
You know the length of hypotenuse parts 9 and 16, at which the hypotenuse of a right triangle is divided by a height. The task is to find the lengths of the sides of the triangle and the length of line x. This assignment was part of the Massachusetts Inst
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