The inscribed angle theorem of polygon problems
Number of problems found: 13
- 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? - 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. - 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.
- 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. - 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. - Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10cm. - 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. - 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 - 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. - 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.
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