Thales' theorem - practice problems - last page
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: 45
- Circumferential angle
Vertices of the triangle ΔABC lay on the circle and are divided into arcs in the ratio 7:8:7. Determine the size of the angles of the triangle ΔABC. - Circumscribing
Find the radius of the circumscribed circle to the right triangle with legs 6 cm and 3 cm. - 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?
Is it true that the height is less or equal to half of the hypotenuse in any right triangle?We apologize, but in this category are not a lot of examples.
Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
