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Adam, You can solve this problem without calculus if you know that a tangent is at right angles to the radius at the point of contact. Thus the line from the centre of the circle to the point of cantact of the tangent to the circle is perpendicular to the tangent and thus has slope 1. Thus the green line in the diagram passes through the origin and has slope 1 and hence its equation is y  1. Find where this line intersects the circle and again use the pointslope line equation to determine the line and put that into the form y = x + a to find the value of a. Harley  


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