Suppose n circles are given in the plane, cutting the plane into pieces. Show that one could color the pieces black and white such that no two pieces sharing an arc have the same color.

Q: A nerd guitarist attempted to measure the auxiliary rectangle from the dips of his preloved electric…

A: The standard form of a hyperbola with the traverse axis on the x axis is x-h2a2-y-k2b2=1.  Here h,k…

Q: If the points A(4,3) and B(x,5) are on the circle with center O (2,3),find the valoe of x

A: Distance between O and A = Distance between O and B = radius.

Q: . Show that a triangle with vertices (1, 4), riangle. Find its area.

A: We will solve the problem.

Q: Show that the points A(-4,9,6) ,B(-1,6,6) and C (0,7,10) from the right angled isoseles triangle

A: Use the equation D=(x2-x1)2+(y2-y1)2+(z2-z1)2 to calculate the magnitude of side AB.…