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Locus of a point equidistant from two concentric circles?
Another circle midway between the originals.
Can a line be tangent to one circle and a secant to the other in concentric circles?
Yes, it can as long as it is not the tangent line of the outermost circle. If it is tangent to any of the inner circles it will always cross the outer circles at two points--so it is their secant line--whereas the tangent of the outermost circle is secant to no circle because there are no more circles beyond that last one.
What is a Venn diagram divisible by 4 and 8?
The Venn diagram consists of a rectangle with two concentric circles. In the inner circle are the multiples of 8. In the outer circle are multiples of 4 which are not also multiples of 8. That is, they are 4 times all odd numbers. Mathematically, that is the set of numbers 4*(2n-1) where n is an integer. Outside the circles, are all the integers that are not divisible by 4.
Find the center of the circle without folding it?
You do not know how to find the centre of a circle. But can you find the centre of a equilateral triangle. If your answer is yes, then you make a concentric circle and a triangle. Let me explain. First take a random point on the circle. Now from that point draw two 60 degree angles. Then take the two points where those 60 degree angles meet the circumference. Now you have three points. Now join them. You get an equilateral triangle.Now take an angle and bisect it. Do the same with the other two angles. Are they not concurrent (meet at a same point?) Well now the place they meet is the centre of the triangle. And since the centre of the triangle and the circle is same, that is the centre.
What is the area between two concentric circles having diameters 10 and 18 meters?
For a circle, A = pi*r2 where A is the area and r the radius. For an anuulus, A = pi*(R2 - r2) where R is the outer radius and r the inner radius. So, A = pi*(182 - 102) = 703.717 (to 3 dp)
