Thales' theorem - practice problems - page 2 of 3

Direction: Solve each problem carefully and show your solution in each item.

Number of problems found: 46

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.
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?
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.
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?
Spectators 7562
The theater has the shape of a semicircle, and the 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?
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.
Same area
There is a given triangle. Construct a square of the same area.
Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
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.
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.
Complete construction
Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of the legs.
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?
Construct 1
Construct a triangle ABC, a = 7 cm, b = 9 cm with a right angle at C, and construct the axis of all three sides. Measure the length of side c (and write).
construction triangle problem
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,. ..
Triangle SSA
Construct a triangle ABC if |AB| = 5cm v_a = 3cm, CAB = 50 °. It is to create the analysis and construction steps.
Inscribed triangle
A circle is an inscribed triangle, and its vertices 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.
Right triangle
Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
The chord
A chord passing through its center is the side of the triangle inscribed in a circle. What size are a triangle's internal angles if one 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 sees the bridge from the largest angle?

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