Inscribed angle theorem - practice problems - page 2 of 3
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: 54
- 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?
- Calculate 9701
In the triangle, the side length AB = 6 cm, the height per side c = 5 cm, and the angle BCA = 35°. Calculate sides a b.
- 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.
- 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?
- Spectators 7562
The theater has the shape of a semicircle, and the 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 with sides lengths> a = 30cm and b = 12.5cm, the right angle is at vertex C. Calculate the radius of the inscribed circle.
- Conditions 7186
Given an isosceles right triangle ABS with base AB. On a circle centered at point S and passing through points A and B, point C lies such that triangle ABC is isosceles. Determine how many points C satisfy the given conditions and construct all such point
- Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10cm.
- Triangle - many properties
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.
- 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.
- 30-gon
The radius of the inscribed circle is 15cm at a regular 30-gon. Find the side length a, circle radius R, circumference, and area.
- Circular segment
Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm, and the angle α = 60°. Help formula: S = 1/2 r². (Β-sinβ)
- Diagonals
Draw a square ABCD whose diagonals have a length of 6 cm.
- Pentagon
Calculate the length of a regular pentagon's side, circumference, and area, inscribed in a circle with a radius r = 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?
- Intersection 3383
A regular 15-angle is given. A triangle is formed if we connect points 3 and 7, 13 and 10. The vertices are 3 and 13, and the lines' intersections are 3.7 and 13.10. We are to determine the angle size formed by sides 3.7 and 13.10. These numbers indicate
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