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The square ABCD has sides of length 1 unit and it is split into three triangles by the lines BP and CP. If P is the midpoint of AD, find the radii of the inscribed circles of these triangles.
Now suppose the lengths AP and PD are (1- p) and p respectively. Find the radii of the three circles r_1, r_2and r_3 in terms of p and plot, on the same axes, the graphs of r_1, r_2 and r_3 as p varies from 0 to 1. Can the ratio of the radii r_1 : r_2 : r_3 ever take the value 1:2:3?
A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?
A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?
Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?