## Challenge 361: Right-angle Ratio

An isosceles right-angled triangle has sides AB and AC which are both 10 units long.

M is the midpoint of AB.

X is the point on CM (inside the triangle) for which angle AXB is a right angle.

Find the ratio MX : XC.

Bonus question - what is MX : XC if X lies on CM extended, outside triangle ABC?