There-are-two-circles-C-of-radius-1-and-C-r-of-radius-r-which-intersect-on-a-plain-At-each-of-the-two-intersecting-points-on-the-circumferences-of-C-and-C-r-the-tangent-to-C-and-that-to-C-r-fo

Question Number 145370 by imjagoll last updated on 04/Jul/21

There are two circles, C of radius 1 and C_{r}

of radius r which intersect on a plain

At each of the two intersecting

points on the circumferences of

C and C_{r}, the tangent to C and

that to C_{r} form an angle 120 ° outside

of C and C_{r} . Fill in the blanks

with the answers to the following

questions

(1) Express the distance d between

the centers of C and C_{r} in terms

of r

(2) Calculate the value of r at

which d in (1) attains the minimum

(3) in case (2) express the area

of the intersection of C and C_{r}

in terms of the constant π