Inscribed angle theorem - practice problems
The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle. An inscribed angle is the angle formed in the interior of a circle when two secant lines intersect on the circleDirection: Solve each problem carefully and show your solution in each item.
Number of problems found: 56
- Angle over circle
In the figure, O is the center of the circle and AB is tangent at B. If angle OAB is 28 degrees find angle AOB. Figure is not scaled. - Calculate 449
Calculate the size of the angle formed by 2 lines on the dial and formed by connecting the points 7.2 and 1.4. - Central angle
A circle k with a center at point S and a radius of 6 cm is given. Calculate the size of the central angle subtended by a chord 10 cm long. - Clock face
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. - Quadrilateral 82395
The points ABC lie on the circle k(S, r) such that the angle at B is obtuse. How large must the angle at vertex B of quadrilateral SCBA be so that this angle is three times greater than the interior angle ASC of the same quadrilateral? - 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. - Circumscribed circle
In triangle ABC, we know a = 4 cm, b = 6 cm, γ = 60°. Calculate the area and radius of the inscribed and circumscribed circle.
- Triangle 80994
In the triangle, ABC, the angles alpha and beta axes subtend the angle phi = R + gamma/2. R is a right angle of 90°. Verify. - 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. - Corresponding 79314
On the circular face of the clock, we connect the points corresponding to the numbers 2, 9, and 11, which creates a triangle. Calculate the sizes of all the interior angles of that triangle. - Triangle 73464
The given line is a BC length of 6 cm. Construct a triangle so that the BAC angle is 50° and the height to the side is 5.5 cm. Thank you very much. - Calculate 71744
The triangle that connects on the dial: a) 2,7,9 b) 3,6,10 Calculate the size of the interior angles. - Three
Three points are given: A (-3, 1), B (2, -4), C (3, 3) a) Find the perimeter of triangle ABC. b) Decide what type of triangle the triangle ABC is. c) Find the length of the inscribed circle - 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. - Construction 55311
Construct a KLM triangle where side k is 6.7 cm, the line to the k side is 4.1 cm, and the LKM angle is 63 degrees. Write the construction procedure.
- Length of the chord
Calculate the length of the chord in a circle with a radius of 25 cm and 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 spectators, P, Q, R, S, and T, see the stage at the greatest viewing angle? - Angles - clock hands
Find the angle that the large hand makes with the small hand of the clock - the central angle at 12:30. Find the magnitude 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 apart. - Dodecagon
Calculate the size of the smaller angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees. - 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.
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