Geometry - examples
How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm and Paul is from the tower distant 20 m.
- Vector 7
Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
- 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 ?
Are two right triangles similar to each other if the first one has a acute angle 10° and second one has acute angle 50°?
Is right that in any right triangle height is less or equal half of the hypotenuse?
How many parts of line divide 5 (different) points that lie on it?
Line p passing through A[-10, 1] and has direction vector v=(2, 4). Is point B[-20, -19] on the line p?
Which of the pairs of numbers on the number line encloses the longest segment: ?
Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
- Pizza master
Master says that he can splits pizza to 16 parts by five equals straight cuts. Is it possible?
On how many parts divide plane 8 parallels?
- Linear independence
Determine if vectors u=(3; -3) and v=(0; 3) are linear Linear dependent.
- OK circle
Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 17 and one cathetus long 1.
Can we construct a line segment, if we know: center and one end point
Determine coordinates of the vector u=CD if C[13;-8], D[-19,-13].
- Shadow and light
Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall?
Determine the radius of the circumscribed circle to the right triangle with legs 3 cm and 3 cm.
- See harmonics
It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases.
- Similarity of squares
The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ?
- Lie/do not lie
The function is given by the rule f(x) = -x-12. Determine whether point D[-4; 2] lies on this function. Solve graphically or numerically and give reasons for the your answer.