CircleHardBloom L3
Question
Consider 3 non-collinear points $A,B,C$ with coordinates $(0,6),(5,5)$ and $( - 1,1)$ respectively. Equation of a line tangent to the circle circumscribing the triangle $ABC$ and passing through the origin is:
Options
A.$2x - 3y = 0$
B.$3x + 2y = 0$
C.$3x - 2y = 0$
D.$2x + 3y = 0$
Solution
[Key Concept: Three given points: use the circumcircle / required locus condition directly.]
Note that the $ABC$ is right angled at $A$
∴ equation of circle
$$\begin{matrix} & \ (x + 1)(x - 5) + (y - 1)(y - 5) = 0 \\ & x^{2} + y^{2} - 4x - 6y - 5 + 5 = 0 \\ & x^{2} + y^{2} - 4x - 6y = 0 \end{matrix}$$
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