1976 AHSME Problems/Problem 18
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Extend 
until it touches the opposite side of the circle, say at point 
By power of a point, we have 
so 
Therefore, 
Now extend 
in both directions so that it intersects the circle in two points (in other words, draw the diameter of the circle that contains 
). Let the two endpoints of this diameter be 
and 
where 
is closer to 
Again use power of a point. We have 
But if the radius of the circle is 
we see that 
and 
so we have the equation 
Solving gives 
