Thales' theorem - practice for 13 year olds
Number of problems found: 24
- Right-angled 78394
A right-angled triangle was inscribed in a circle with a diameter of 20 cm, whose hypotenuse is the circle's diameter and has the largest possible area. Calculate the area of this triangle. - Triangle 67504
Sestroj triangle HOP, if o = 6 cm, h = 8 cm and | PHO | = 90 ° - Quadrilateral 67384
Construct a quadrilateral ABCD if AB = 10cm, AD = 6cm, DC = 6.5cm and angle BCD = 90 degrees - Hypotenuse 65744
Construct a right triangle ABC with the hypotenuse AB: a) | AB | = 72 mm, | BC | = 51 mm b) | AB | = 58 mm, | AC | = 42 mm
- Draw triangle
Construct right triangle MNO with hypotenuse o = 5 cm and angle MNO = 37° - Construct
Construct a rhombus ABCD with side a = 7cm, b = 5cm, whose diagonal e is perpendicular to side b. - Triangle 45671
Draw a right triangle with side a = 5 cm, c = 8 cm. The right angle is at vertex C. What is the size of side b? * - The amphitheater
The amphitheater has the shape of a semicircle, the spectators sit on the perimeter of the semicircle, and the stage forms the diameter of the semicircle. Which of the spectators, P, Q, R, S, T, sees the stage at the greatest viewing angle? - Construct rhombus
Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm
- 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. - 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 - Diagonals at right angle
In the trapezoid ABCD, this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD? - Tangent 6770
A circle k (S; 2.5 cm) and a point L are given if | SL | = 4cm. Make a tangent to the circle passing through point L. - Two heights and a side
Construct triangle ABC when the given side is c = 7 cm, height to side a va = 5 cm, and height to side b: vb = 4 cm.
- Distance 4527
There are two points, K and L, KL = 4 cm. Draw a line p passing through point K and having a distance of 4 cm from point L. - Tangents construct
The circle k is given k (S; 2.5 cm) and an outer line p. Construct a tangent t of the circle that has a line p angle 60°. How many solutions have the task? - The chord
A chord passing through its center is the side of the triangle inscribed in a circle. What size are the internal angles of a triangle if one of them is 40°? - The bridge
Across the circle, the lake passes through its center bridge over the lake. At three different locations on the lakeshore are three fishermen, A, B, and C. Which of the fishermen see the bridge from the largest angle? - Semicircle
The semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
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