A and B are two points on a circle centered at the origin.

Question

A (9,5) and B (5,-9) are two points on a circle centered at the origin. 

a) Determine an equation for the circle.

b) Determine the midpoint C of chord AB.

c) Show that the right bisector of chord AB passes through the centre of the circle.

Answer 1

a)

x² + y² = 106  (that is 9² + 5²)

 

b)

Use the midpoint formula

 

c) 

Draw radii to A and B.

Right bisector creates two congruent triangles.