circumcircle of point of contact of tangent to a circle

Question

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?

score 2 · Accepted Answer · edited Apr 13 '17 at 12:20

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.

edited Apr 13 '17 at 12:20

Community

1

answered Feb 25 '17 at 11:14

robjohn

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circumcircle of point of contact of tangent to a circle

1 Answers1