Thales' theorem - practice problems - last page

Instructions: Solve each problem carefully and provide a detailed solution for every item.

Number of problems found: 46

Semicircle
The semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
Circumferential angle
Vertices of the triangle ΔABC lay on the circle and are divided into arcs in the ratio 10:8:7. 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 leg long 17. Calculate the radius (circumradius) of the circle described.
Rectangle
In a rectangle with sides 8 and 9, a diagonal is drawn. What is the probability that a randomly selected point inside the rectangle is closer to the diagonal than to any side of the rectangle?
Height
Is it true that in any right triangle, the altitude to the hypotenuse is less than or equal to half the hypotenuse?

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