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The radius of a circle changes by 1 mm, how will the length of the circle change?
How many diagonals the n-gon has?
Can a closed polyline have sides the lengths of which are 1, 2, 3, 4 and 11 meters?
Two circles are given. Their radiuses are R1 and R2. The distance between their centers is d1 (d1>R1+R2). What is the minimal and maximal distance between points X and Y which belong to these circles?
Where the points are located, if for these points x=0 and y=0?
The planes a and b are parallel to the plane c. Can planes a and b intersect?
Straight lines a and b are given. These lines don’t belong to the same plane. Can we draw a straight line, which is parallel to each of these lines?
Three points belong to the same straight line. Can we build a plane, which contains these three points? Explain your answer.
A cone has a slant side measure (m) and a semi-vertical angle 2(x). Prove that the measure r of the radius of the sphere inscribed in the cone is given by:
r = (m sin(4x))/2(1+sin(2x))
There are four points, which don’t belong to the same plane. Can any three of these points belong to the same straight line? Explain your answer.
