The straight line x−2y+1=0   intersects theCircle x2+y2=25 in points  P and Q. The coordinates of the point of intersection of tangents drawn at P and Q to the circle are

Let the required point be    Rx1,y1 Then,  PQis the chord of contact of tangents drawn from Rx1,y1  tox2+y2=25 So, the equation of   PQ  is  xx1+yy1=25This equation and    x−2y+1=0  represent the same line. ∴ x11=y1−2=−251⇒x1=−25 and  y=50Hence, the required point is  ( - 25, 50)