Inscribed angle theorem - practice for 13 year olds
Number of problems found: 23
- Corresponding 82704
On the circular face of the clock, we connect the points corresponding to the numbers 2, 5, and 9 to each other, which creates a triangle. Calculate the sizes of all interior angles. - Calculate 82282
Calculate the sizes of the interior angles in the triangle whose vertices are the points marked by the numbers 1, 5, and 8 on the clock face. - Parallelogram 80761
Construct a parallelogram ABCD if a=5 cm, height to side a is 5 cm, and angle ASB = 120 degrees. S is the intersection of the diagonals. - Quadrilateral in circle
A quadrilateral is inscribed in the circle. Its vertices divide the circle in a ratio of 1:2:3:4. Find the sizes of its interior angles.
- Length of the chord
Calculate the length of the chord in a circle with a radius of 25 cm with a central angle of 26°. - 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? - Determine 28391
Determine the angle that the large hand makes with the small hand of the clock - the central angle at 12:30. Determine the size of the smaller angle (if possible). (Help: it's enough if you calculate how big an angle the hands make if they are 1 minute ap - Interior angles
In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees, and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles. - Clock hands
Calculate the internal angles of a triangle whose vertices lie on the clock's 2, 6, and 11 hours.
- Hexagonal pyramid
Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm. - Triangle 15123
In triangle ABC, we know the angle BAC = 50 degrees. What is the angle between the axis of the angle ACB and the axis of the angle CAB? - Quadrilateral 8405
Calculate the magnitude of the largest inner angle and the deviation of the diagonals in the quadrilateral, whose vertices correspond to points 1, 5, 8, and 12 on the dial. - Hexagon in circle
Calculate the radius of a circle whose length is 10 cm greater than the circumference of a regular hexagon inscribed in this circle. - RT - inscribed circle
In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at vertex C. Calculate the radius of the inscribed circle.
- Diagonals
Draw a square ABCD whose diagonals have a length of 6 cm. - Regular n-gon
Which regular polygon has a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm? - Pentagon
Within a regular pentagon ABCDE point, P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch. - Circular pool
The pool's base is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length of 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool? - 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°?
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