Copy of Problem 2
Problem 2 of the Kumanokotai Shrine Sangaku
AB is the diameter of a semicircle with radius r1.
C and D are points on the circumference of this semi circle.
AC and BD are tangents to the large circle that passes through C, D and I with radius r2.
Triangle ABE has an inscribed circle with radius r3.
The circle with radius r4 touches lines AD and BC and the semicircle at point F.
Given
a) Find r2 in terms of r1.
For extra challenge:
b) Find r3 in terms of r1.
c) Find r4 in terms of r1.
d) Write down the ratio of r1 : r2 : r3 : r4