![]() ![]() ![]() ![]() If θ = 90 degrees, things should be treated separately but then (0.5)θ = 45 degrees. According to the question, m will never be zero, otherwise there will be infinitely many or no C. ∴ $C$ is located at $(OC, (0.5)θ)$ in polar co-ordinates. Together with $\angle CA’O = π – θ$, $OC$ can be found by cosine law. Note also that $⊿A’OC$ is isosceles with $A’O = A’C = a$. In the figure, $\angle BCO = \angle A'CO = \angle COA’ = (0.5)θ$ $P(t_a)=(\cos(t_a),\sin(t_a))$ for $A$ and similarly for $B.$ The values for these $t$ are Rewrite each of $A,B$ in polar coordinates as $(r_a,\theta_a),\ (r_b,\theta_b).$ For each of $A,B$ there are then two points on $C$ where the tangents from $A$ or $B$ meet $C$, say they are at $t_a,t_b$ in the sense that their coordinates are e.g. To begin with we may assume the circle $C$, center $(0,0),$ has radius $1$ (divide all coordinates by the circle radius, then remultiply at the end). ![]()
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