Planimetrics + real numbers - practice problems
Number of problems found: 40
- Complex plane mapping
Show that the mapping w = z +c/z, where z = x+iy, w = u+iv, and c is a real number, maps the circle |z| = 1 in the z-plane into an ellipse in the (u, v) plane. - Estate
Semicircle estate must be a fence. The straight section has a 26 meters long fence. How many meters of the fence should we buy? - Described
Calculate the perimeter of the circle described by a triangle with sides 478, 255, 352. - Sea
How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km). - Rail turn
The curve radius on the railway line is 532 m. The length of the rail track on it is 818 m. How many degrees is the angle ASB if A and B are boundary points and S is the center of the arc curve? - Medians
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 25 cm and tb=30 cm. - Quarter circular
The wire hooked around the perimeter of the quarter-circular arc has a length of 5π+20. Determine the radius of the circle arc. - Euclid1
The right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c? - Hypotenuse and height
In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both triangle legs. - Rectangle
The rectangle is 21 cm long and 38 cm wide. Find the radius of the circle circumscribing the rectangle. - Area 4gon
Calculate the area of 4-gon, two, and the two sides are equal and parallel with lengths 11, 5, 11, and 5. Inner angles are 45°, 135°,45°, 135°. - Square 2
Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate the area of the square ABCD. - Wire D
Wire length 1 m is bent to form a semicircle circuit (including the diameter). Determine the radius of the semicircle. - Rhombus ABCD
Rhombus ABCD, |AC| = 63 cm, |BD| = 50 cm. Calculate the perimeter of the rhombus ABCD. - Diagonals of the rhombus
Calculate the height of the rhombus whose diagonals are 18 cm and 6 cm. - Garden
How many steps of 76 cm circumvent square garden with area 1.8 ha? - Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm², and if a: b: c = 12:7:18 - Rectangle SS
The perimeter of a rectangle is 268 cm, and its diagonal is 99.3 cm. Determine the dimensions of the rectangle. - Gimli Glider
Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintains optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long it takes for a plane to hit the ground from engine failure. - Rectangle
In rectangle ABCD with sides, |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio (|PB|)/(|DP|).
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