# 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 circleDirection: Solve each problem carefully and show your solution in each item.

#### Number of problems found: 45

- Isosceles trapezium

Trapezoid YUEB (YU||EB) is isosceles. The size of the angle at vertex U is 49 degrees. Calculate the size of the angle at vertex B. - Semicircle

The semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC? - Clock hands

Calculate the internal angles of a triangle whose vertices lie on the clock's 2, 6, and 11 hours. - Diagonals

Draw a square ABCD whose diagonals have a length of 6 cm - 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. - 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. - Clock face

A clock face is drawn on paper. Straight lines connect numbers 10 and 5 and 3 and 8. Calculate the size of their angles. - 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? - 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. - Inscribed circle

Calculate the magnitude of the BAC angle in triangle ABC if it is three times less than the angle BOC, where O is the center of the circle inscribed in triangle ABC. - 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. - Calculate 71744

The triangle that connects on the dial: a) 2,7,9 b) 3,6,10 Calculate the size of the 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. - 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 - 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? - 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. - 30-gon

At a regular 30-gon, the radius of the inscribed circle is 15cm. Find the side length a, circle radius R, circumference, and area. - 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? - 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°? - 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°.

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