# Geometry - examples

- Find parameters

Find parameters of the circle in the plane - coordinates of center and radius: ? - Lighthouse

Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea. - Trapezium diagonals

It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC. - MG=7x-15,

MG=7x-15, FG=33, x=? Point M is the midpoint of FG. Find unknown x. - Midpoint 6

FM=8a+1, FG=42, a=? Point M is the midpoint of FG. Find unknown a. - Midpoint 5

FM=3x-4, MG=5x-26, FG=? Point M is the midpoint of FG. Use the given information to find the missing measure or value. - Find midpoint

FM=5y+13, MG=5-3y, FG=? M is the midpoint of FG. Use the given information to find the missing measure or value. - A screen

A screen is 1680 x 1050 pixels. What are the coordinates (and size in pixels) of an centered area which is exactly 33% of the screen size? - Rectangle

In rectangle with sides 10 and 8 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle? - 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 ? - Circle arc

Circle segment has a circumference of 135.26 dm and 2096.58 dm^{2}area. Calculate the radius of the circle and size of central angle. - 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. - Cone

Circular cone of height 15 cm and volume 5699 cm^{3}is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut. - 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 70° and second one has acute angle 20°? - 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.

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