# Circle + right triangle - examples - page 2

1. Shooter The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?
2. Nine-gon Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
3. Elevation What must be the elevation of an observer in order that he may be able to see an object on the earth 782 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
4. The bridge Across the circle lakepasses through its center bridge over the lake. At three different locations on the lake shore are three fishermen A, B, C. Which of fishermen see the bridge under the largest angle?
5. Inscribed rectangle The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
6. Cathethus and the inscribed circle In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
7. Horizon The top of a lighthouse is 17 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
8. Right triangle Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
9. Goat Meadow is a circle with radius r = 19 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow?
10. Chord In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord?
11. Horizontal Cylindrical Segment How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank?
12. Arc Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m.
13. Circle On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN.
14. Hexagon 5 The distance of parallel sides of regular hexagonal is 61 cm. Calculate the length of the radius of the circle described to this hexagon.
15. Semicircle In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
16. The cone The lateral surface area of the cone is 4 cm2, the area of the base of the cone is 2 cm2. Determine the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base ci
17. Common chord Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles?
18. Chord AB What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
19. 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 legs.
20. Moon We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.

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