Thursday, March 26, 2026

Mensa Algrebra and Analytic Geometry (Circle) Problem

 




The circle in this problem is defined by the equation:

 (x - 132) 2 -  (y - 132) 2 = 24, 649  

The circle intersects the y-axis at points A and B as shown.

The point A has a greater y-value than B.

The line AC is a diameter.

M and N are points on the circle such that the angles:

< ACM =  < ACN  =  p /4   radians.

What are the Cartesian coordinates of M and N?

Hint: You may need to apply the inscribed angle theorem which states:

An inscribed angle is equal to one half the central angle that intercepts the same arc.

You may also need to do a circle reconstruction to incorporate the points M and N in relation to each other and their lines to the diameter. 



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