# Geometry - problems

- Right triangle from axes

A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 sq. Units . The segment passes through the point ( 5,2). What is the slope of the line segment. ? - Points collinear

Show that the point A(-1,3), B(3,2), C(11,0) are col-linear. - Shadow

A meter pole perpendicular to the ground throws a shadow of 40 cm long, the house throws a shadow 6 meters long. What is the height of the house? - Two chords

There is a given circle k (center S, radius r). From point A which lies on circle k are starting two chords of length r. What angle does chords make? Draw and measure. - Prove

Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - Forces

In point O acts three orthogonal forces: F_{1}= 20 N, F_{2}= 7 N and F_{3}= 19 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: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ? - Triangle

Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles. - Railways

Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters. - 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? - Similarity

Are two right triangles similar to each other if the first one has a acute angle 40° and second one has acute angle 50°? - Hexagon

There is regular hexagon ABCDEF. If area of the triangle ABC is 22, 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 8.7%. 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 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of the larger triangle. - Speed of Slovakian trains

Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H - Center

Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18]. - Crossroads

The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 43 km/h and ambulance 52 km/h. Calculate such a relative speed of the ambulance moves to the car. - OK circle

Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17. - Climb

Road has climbing 1:27. How big is a angle corresponds to this climbing? - Angle between lines

Calculate the angle between these two lines: ? ?

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