I think this question requires the use of the distance between a line and a point formula! Since the radius will be the line perpendicular to the tangent, to the origin, you can literally plug in the values and a radius should pop out.
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Where A=4, B=-3, C=-5, x=0 and y=0
I think the radius turns out to be 1!
Jake
This is definitely the correct method, since we know the centre of the circle we just need the radius, which can be obtained through this formula, and it does indeed end up as 1!
Rui's method above is a cool proof, but far beyond what is required here. At this level, intuition is absolutely fine. The perpendicular distance to a line is the shortest distance to said line. Since it is the shortest distance, a circle with a radius equal to that distance will clearly only touch the line once.
So basically, in a 2 Unit Exam, just the formula would suffice, but if you are doing 3 unit or above Rui's proof is good to understand