Inscribed angle theorem of Circle Problems - page 2 of 3
Number of problems found: 41
- 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. - Point construction
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 - Clock angle
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) - 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? - Inscribed circle
XYZ is a right triangle with a right angle at the vertex X and an inscribed circle with a radius of 5 cm. Find the area of the triangle XYZ if XZ = 14 cm. - 6 regular polygon
A regular six-sided polygon has a side 5 cm long. Calculate its area. Compare how many more cm² (square centimeters) has a circle inscribed the 6-gon. - Complete construction
Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of the legs. - 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? - Inscribed triangle
A circle is an inscribed triangle, and its vertices divide the circle into three arcs. The length of the arcs is in the ratio 2:3:7. Find the interior angles of a triangle. - Circle inscribed
Calculate the perimeter and area of a circle inscribed in a triangle measuring 3, 4, and 5 cm. - The chord
A chord passing through its center is the side of the triangle inscribed in a circle. What size are a triangle's internal angles if one is 40°? - Circle section
An equilateral triangle with side 33 is an inscribed circle section whose center is in one of the triangle's vertices, and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio between the circumference to the circle sector a - Semicircle
The semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC? - Circumferential angle
Vertices of the triangle ΔABC lay on the circle and are divided into arcs in the ratio 10:8:7. Determine the size of the angles of the triangle ΔABC.
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