Triangle + Thales' theorem - practice problems - page 2 of 3
Number of problems found: 41
- Semicircle
The semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC? - 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,. .. - OK circle
The right triangle has hypotenuse long 33 and one cathetus long 17. Calculate the radius (circumradius) of the circle described. - 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. - Same area
There is a given triangle. Construct a square of the same area. - 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 - 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. - 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.
- 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. - 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. - Construct 80719
Construct a rectangle ABCD if a = 8cm and the length of the diagonal AC is 13cm. Measure the length of the sides of the rectangle. - 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? - 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°?
- Quadrilateral 67384
Construct a quadrilateral ABCD if AB = 10cm, AD = 6cm, DC = 6.5cm and angle BCD = 90 degrees - 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 - Construct
Construct a rhombus ABCD with side a = 7cm, b = 5cm, whose diagonal e is perpendicular to side b. - Construct rhombus
Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm - 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
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