# Practice problems of the inscribed angle theorem

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 circle#### Number of problems found: 40

- Triangle 73464

The given line is a BC length of 6 cm. Assemble 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 so that its vertices divide the circle 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 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? - Dodecagon

Calculate the size of the smaller of the 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. - 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

In the quadrilateral, whose vertices correspond to points 1, 5, 8, and 12 on the dial, calculate the magnitude of the largest inner angle and the deviation of the diagonals. - Isosceles 7566

A right isosceles triangle is inscribed in the circle with r = 8 cm. Find triangle area S. How many percent does the triangle occupy the area of the circle? - Spectators 7562

The theater has the shape of a semicircle. A podium is the diameter of a semicircle. Spectators K, L, M, N, and O, sit around the perimeter. Who sees the podium at the greatest angle? - 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 the vertex C. Calculate the radius of the inscribed circle. - Nonagon

Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10cm - Circumscribed 6568

In a right triangle ABC with a right angle at the vertex C, it is given: a = 17cm, Vc = 8 cm. Calculate the length of the sides b, c, its area S, the perimeter o, the length of the radii of the circles of the triangle circumscribed by R and inscribed r an - Calculate 6539

Calculate the magnitude of the angle formed by the lines p and q, which connect 1, 6 (line p), and 5, 8 (line q) on the clock face

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