Circle + Thales' theorem - practice problems
Number of problems found: 31
- Right-angled 78394
A right-angled triangle was inscribed in a circle with a diameter of 20 cm, whose hypotenuse is the circle's diameter and has the largest possible area. Calculate the area of this triangle. - 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 described
The circle radius described in the right triangle with a 6 cm long leg is 5 cm. Calculate the circumference of this triangle. - Calculate 16223
The following elements are known in the right triangle ABC: a = 10 cm, height to side c h = 9.23 cm. Calculate o, R (radius of the inscribed circle), r (radius of the inscribed circle).
- Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the 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. - 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. - The amphitheater
The amphitheater has the shape of a semicircle, the spectators sit on the perimeter of the semicircle, and the stage forms the diameter of the semicircle. Which of the spectators, P, Q, R, S, T, sees the stage at the greatest viewing angle?
- Parallels and one secant
There are two different parallel lines, a, b, and line c, that intersect the two parallel lines. Draw a circle that touches all lines at the same time. - 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. - 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? - 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? - 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.
- 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? - Same area
There is a given triangle. Construct a square of the same area. - Draw triangle
Construct right triangle MNO with hypotenuse o = 5 cm and angle MNO = 37° - 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. - 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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