Problem 6
A, B, C and D are points lying on the circumference of the circle that has radius r.
There is a line of symmetry through AC so arc AD is congruent to AB and meet at point A.
Also arc DC is congruent to arc CB and meet at point C.
Circles with centres O1 and O2 are kissing circles and also touch two other arcs each as shown in the
diagram, these are congruent circles with a radius of r1.
a is the length of the widest parts of the shape enclosed by the arcs of the circle with radius r and the
arc of a circle with radius r2.
b is the length of the widest parts of the shape enclosed by the arcs of the circle with radius r and the
arc of a circle with radius r3.
Find the radius of the small red circle r1 in terms of a and b.
