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# C is a circle with centre the origin. A tangent to C passes through the points (-30, 0) and (0, 10) Work out an equation of C. You must show all your working?

Origin at 0,0 means equation is X2 + y2 = r2 We just need to find r. A little bit of trignometry, right angle triangles and there you go. First we find the angle at left edge of triangle boung by two axes and base 30 h 10. Tan theta = 10/30 Calculator, Theta = 18.4 degrees Then you take the triangle bound by x axis 30 And radius r With angle 18.4 Sin 18.4 = r/30 R comes out to be 9.49 units So that goes back into your equation of circle and there you have it.  H Ali
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