# Geometry - problems - page 6

1. Rhombus
ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
2. Vector
Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
3. Triangle SSA
Construct a triangle ABC if |AB| = 5cm va = 3cm, CAB = 50 °. It is to create the analysis and construction steps.
4. Medians in triangle
Median of isosceles triangle has a length 3 cm. Determine the length of its sides if its perimeter is 16 cm.
5. Right angled triangle 2
LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n
6. Right triangle - leg
Calculate to the nearest tenth cm length of leg in right-angled triangle with hypotenuse length 9 cm and 7 cm long leg.
7. Tangents construct
Circle is given k (S; 2.5 cm) and an outer line p. Construct a tangent t of the circle that has with a line p angle 60°. How many solutions has the task?
8. Three points
Mark three points E, F and G in the plane not lie on one line. a) Draw a line segment FG b) Construct halfline (ray) EG c) Draw a line EF
9. Mine
What is temperature in the mine at a depth of 1160 m, where at depth 9 m is 11°C and every 100 m, the temperature increases by 0.7°C?
10. Line segment
For the line segment whose endpoints are L[-1, 13] and M[18, 2], find the x and y value for the point located 4 over 7 the distance from L to M.
11. Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
12. Parabola
Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)
13. Center of gravity
The mass points are distributed in space as follows - specify by coordinates and weight. Find the center of gravity of the mass points system: A1 [14; -2; 5] m1 = 10.2 kg A2 [-2; -16; 7] m2 = 13.6 kg A3
14. Traffic laws
Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped car at 1.5 m from the wall. The dipped-beam headlights are 60 cm high. At what height on the wa
15. Clock face
clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
16. Inscribed circle
Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
17. Square ABCD
Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4].
18. Square
Draw a square on the edge of a = 4 cm. Mark the center of symmetry S and all axes of symmetry. How many axes of symmetry does? Write down.