Tangents drawn from the point $P(1, 8)$ to the circle $x^2 + y^2 - 6x - 4y - 11 = 0$ touch the circle at the points A and B. Will the circumcircle of triangle $PAB$ pass through $(3,2)$ or the center of the first circle?
circumcircle of point of contact of tangent to a circle
0
$\begingroup$
geometry
analytic-geometry
circles
coordinate-systems
-
0Draw a picture. – 2017-02-25
1 Answers
2
Hint: Consider the construction of the points of tangency using straight-edge and compass. See this question. A circle is drawn so that $(1,8)$ and $(3,2)$ are at opposite ends of one of its diameters.
