MathDB

The opposite sides of a quadrilateral inscribed in a circle intersect at points

K

and

L

. Let

F

be the midpoint of

KL

E

and

G

be the midpoints of the diagonals of the given quadrilateral. It is known that

FE = a

FG = b

. Calculate

KL

in terms of

a

and

b.

(It is known that the points

F

E

and

G

lie on the same straight line. This is true for any quadrilateral, not necessarily inscribed. The indicated straight line is sometimes called the Newton−Gauss line. This fact can be used without proof in proving the problem, as it is known).

Problem Statement