The radii of the incircle and the circumcircle of a quadrilateral are 7 and 12. Find the distance between the centers of the two circles.
(In reply to
re: the right starting point?  kite solution by Brian Smith)
I tried starting with an isosceles trapezoid, which always has a circumcircle and can be easily adjusted to have an incircle. This proved difficult so I switched and also went with a right kite.
With sides a and b we have a^2+b^2=24^2 and ab/(a+b)=7
From which a+b=32, ab=224 and the distance sought satisfies
d^2=(7a/2)^2+(7b/2)^2
d^2=18
d=sqrt(18)=3sqrt(2)

Posted by Jer
on 20191026 13:49:50 