MathDB

constant quantity of chords inside circle

Source: Ukraine 1999 Grade 9 P7

May 10, 2021

geometry

Problem Statement

Let

M

be a fixed point inside a given circle. Two perpendicular chords

AC

and

BD

are drawn through

M

, and

K

and

L

are the midpoints of

AB

and

CD

, respectively. Prove that the quantity

AB^2+CD^2-2KL^2

is independent of the chords

AC

and

BD