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You can put this solution on YOUR website!
I don't know how you are expected to solve the problem,
\n" ); document.write( "but here goes my drawing-heavy, wordy solution.
\n" ); document.write( "Here are
\n" ); document.write( "the circle
\n" ); document.write( "the line
\n" ); document.write( "the perpendicular bisector of PQ, line
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\n" ); document.write( "The equation of the circle shows that it has radius
\n" ); document.write( "The equation of the red line shows that it passes through (0,-3),
\n" ); document.write( "so we know that it crosses the circle at that point.
\n" ); document.write( "The red line also crosses the circle at (-42/50,144/50)=(-0.84,2.88).
\n" ); document.write( "That is not so easy, but substituting
\n" ); document.write( "we get
\n" ); document.write( "with solutions
\n" ); document.write( "Then substituting
\n" ); document.write( "
\n" ); document.write( "From the equation for the blue line, with
\n" ); document.write( "we know that it forms a
\n" ); document.write( "and so it forms that little isosceles right triangle with the x-axis and the y-axis.
\n" ); document.write( "That slope, and the symmetry makes the problem easy.
\n" ); document.write( "(I found it very easy after scratching my head for an hour).
\n" ); document.write( "The point where the blue and red lines intersect is (-1/2,1/2), and I'll call it point R.
\n" ); document.write( "The red line
\n" ); document.write( "so I can call it line RQ.
\n" ); document.write( "We know Q is on that line.
\n" ); document.write( "
\n" ); document.write( "We still do not see line PQ, but we know that
\n" ); document.write( "line PQ is perpendicular to the blue line.
\n" ); document.write( "We also know that
\n" ); document.write( "line PQ passes through P (a point in the circle), and
\n" ); document.write( "through Q, a point in the red line
\n" ); document.write( "Point R, on the perpendicular bisector of PQ,
\n" ); document.write( "is at the same distance from P and Q, and
\n" ); document.write( "is the vertex of isosceles triangle PRQ.
\n" ); document.write( "That blue line perpendicular bisector contains the altitude of PRQ,
\n" ); document.write( "and bisects angle PRQ.
\n" ); document.write( "I could draw line PR (in green),
\n" ); document.write( "as the reflection of the red line RQ on the blue line,
\n" ); document.write( "because I know that PR and RQ make the same angle with the blue line.
\n" ); document.write( "I could even draw the bisector of the other angle formed by PR and RQ.
\n" ); document.write( "I'll draw that one as a black line.
\n" ); document.write( "
\n" ); document.write( "Because they are bisectors of the angles formed by the same red and green lines,
\n" ); document.write( "the blue and black lines are perpendicular.
\n" ); document.write( "The slope of the black line is
\n" ); document.write( "It is all very symmetrical;
\n" ); document.write( "the slopes of the red and green lines are
\n" ); document.write( "and
\n" ); document.write( "I may be missing something, but I see two points that could be P:
\n" ); document.write( "(3,0), where the green line crosses the circle on the right side, and
\n" ); document.write( "(-144/50,42/50)=(-2.88,0.84), where the green line crosses the circle on the left side.
\n" ); document.write( "P=(3,0) would mean Q=(-1,4)
\n" ); document.write( "(Q is 3.5 units up and 0.5 left from R,
\n" ); document.write( "because P is 3.5 units right and 0.5 units down)
\n" ); document.write( "P=(-144/50,42/50) would mean Q=(-8/50,-94/50)
\n" ); document.write( "(both points are 119/50 in one direction and 17/50 in another from R)
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