C1 Coordinate Geometry Help!!!

Hi, please help me through this question.

P (2,-1) Q(6,7)

x^2+y^2-12x-4y+15=0

Find the coordinates of the point, R, where this radius intersects the circle.

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So first I found the equation of the radius of the circle passing through the midpoint of the chord PQ which is x+2y=10

If this radius equation was to intersect the circle wouldn't there be 2 points of intersection?
Because I tried to sub x+2y=10 into the equation of the circle, but I didn't get the right answer. Please Help!