# Thales' theorem - practice problems - page 2 of 3

The Tales theorem says that if A, B, C are points on a circle, where AC is the diameter of the circle, then the angle ABC is the right angle. The Tales circle is the set of vertexes of right angles of right triangles constructed above the diameter of the circle. The Tales theorem results directly from the inscribed angle theorem. Simple proof - the radius joining point C divides a rectangular triangle into two isosceles triangles, and the sum of the angles in each triangle is 180°.Direction: Solve each problem carefully and show your solution in each item.

#### Number of problems found: 44

- 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. 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? - 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). - 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,. .. - 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

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. - 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 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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