PURE MATHS CIRCLES

請求指點,

Consider the line L : y=2a and the circle C : x^2 + y^2 =a , a>0.
Let P be a variable point on L. If the tangents for P to C touch the circle C at points Q and R respectively, show that the mid- point of QR lies on fixed circle and find Q and R respectively, show that mid-point of QR lies on a fixed circle and find center and radius of this circle.