# Thales' theorem + geometry construction problems - math problems

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°.

#### Number of problems found: 9

• 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 a line c that intersect the two parallel lines. Draw a circle that touches all lines at the same time.
• 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.
• Circle tangent It is given to a circle with the center S and radius 3.5 cm. 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 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 with a line p angle 60°. How many solutions have the task?
• Construct 1 Construct a triangle ABC, a = 7 cm, b = 9 cm with right angle at C, construct the axis of all three sides. Measure the length of side c (and write).
• Triangle SSA Construct a triangle ABC if |AB| = 5cm va = 3cm, CAB = 50 °. It is to create the analysis and construction steps.
• 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.

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