# Geometry - examples

- MO Z9–I–2 - 2017

In the VODY trapezoid, VO is a longer base and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm^{2.}Find the area of the entire trapezoid. - Points on line segment

Points P & Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance: between point A and the midpoint of the segment QB. - 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 - Line segment

Cut a line segment of 15 cm into two line segments so that their lengths are in ratio 2:1. What length will each have? - Forces

In point X acts three orthogonal forces: F_{1}= 13 N, F_{2}= 8 N and F_{3}= 15 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - Reverse Pythagorean theorem

Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 73 m, 66 m, 51 m ? Δ DEF: 63 cm, 105 cm, 84 cm ? Δ GHI: 50 dm, 48 dm, 14 dm ? Δ JKL: 31 m, 45 m, 40 m ? Δ MNO: 28 m, 53 m, 45 m ? - Triangle

Triangle KLM is given by plane coordinates of vertices: K[-19, -8] L[8, -12] M[2, -6]. Calculate its area and itsinterior angles. - Railways

Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters. - Similarity

Are two right triangles similar to each other if the first one has a acute angle 10° and second one has acute angle 50°? - Circular pool

The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool? - Hexagon

There is regular hexagon ABCDEF. If area of the triangle ABC is 19, what is area of the hexagon ABCDEF? I do not know how to solve it simply.... - Climb

On the road sign, which informs the climb is 20%. Car goes 5 km along this road. What is the height difference that car went? - Similarity coefficient

The ratio of similarity of two equilateral triangles is 3.9 (ie 39:10). The length of the side of smaller triangle is 3 cm. Calculate the perimeter and area of the larger triangle. - Center

Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[27,-11] B[2,-30] C[11,12]. - Speed of Slovakian trains

Rudolf decided to take the train from the station 'Nová Baňa' to 'Gelnica'. In the train timetables found train R 371 Horehronec : km0Břeclav os.n.05:268Lanžhot05:3205:3214Brodské05:3705:3818Kúty05:4205:4344Malacky05:5906:0082Bratislava hl.st.06:2606:37 - Climb

Road has climbing 1:23. How big is a angle corresponds to this climbing? - OK circle

Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 43 and one cathetus long 21. - Angle between lines

Calculate the angle between these two lines: ? ? - Crossroads

The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 45 km/h and ambulance 58 km/h. Calculate such a relative speed of the ambulance moves to the car. - Height

Is right that in any right triangle height is less or equal half of the hypotenuse?

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