Disclaimer: The answer must be an integer, as all competition problems were designed to yield integral answers.
Hello! Yesterday I underwent a math tournament. There was one problem that was rather difficult in my eyes, and that is the question I am bringing up today.
Let ABCD be a square with side length 24, and suppose M is the midpoint of line AB. Construct a circle centered at C through B and D, and let the tangent line through M to this circle (other than AB) intersect AD again at X. What is the length of AX?
Of course I have drawn ABCD and the circle centered at C as described above (using GeoGebra for my first time :) ). In the image please disregard the values on the X and Y axes (as they clearly do not match up with the length of 24, as seen in the problem).
How would I go about starting this problem? Do we try to find the length of MX and use the Pythagorean Theorem to find AX?