Points A(5,-5), B(-5,5), C(1,7) and D(-7,-1) lie on the circle with equation x^2+y^2=50 show algebraically that AB is the perpendicular bisector of chord CD

Answer 1

Hi Eric,

you should be familiar with some Chord theorems. The perpendicular bisector of a chord should pass through the center of the circle. This implies that if one chord bisects another chord then the first chord should be the diameter. So in order to prove that AB is the perpendicular bisector of CD, we have to prove that AB is the diameter.

From the equation of the circle, we can get the radius.

r= sqrt(50)

r= 5sqrt(2)

Diameter d= 2r=10 sqrt(2)

you have to prove that AB is the diameter of the circle:

by using distance formula you can get the length of AB

when 2 end points (x1,y1) and (x2,y2) are given,

distance= sqrt[(x2-x1)^2+(y2-y1)^2]

if you plug in the values from points A, B you should get distance =10sqrt(2), which is the length of the diameter of the circle.

hope this helps!