A circle C C\,C has centre (8,4)(8, 4)(8,4) and radius 2102\sqrt{10}210. A line L L\,L has equation y=mxy = mxy=mx. The xxx-coordinate of any points of intersection of C C\,C and L L\,L satisfies the equation (m2+1)x2−(8m+16)x+40=0(m^2 + 1)x^2 - (8m + 16)x + 40 = 0(m2+1)x2−(8m+16)x+40=0. The values of m m\,m for which L L\,L is tangent to C C\,C are 3 and −13\displaystyle -\frac{1}{3}−31.
Two lines are drawn from the origin which are tangents to CCC. Find the coordinates of the points of contact between the tangents and CCC.
292 exam-style questions on Edexcel A Level Maths Circles, covering 6.1 Midpoints and Perpendicular Bisectors, 6.2 Equation of a Circle, 6.3 Intersections of Straight Lines and Circles, 6.4 Use Tangent and Chord Properties, and 6.5 Circles and Triangles. Each one has a worked solution and a mark scheme showing where the marks go.