Geometry  Circles and tangents
posted by Knights .
Two circles of radius 1 are externally tangent at Q . Let PQ and QR be diameters of the two circles. From P a tangent is drawn to the circle with diameter QR , and from R a parallel tangent is drawn to the circle with diameter PQ . Find the distance between these two tangent lines.
Could someone help me please, I tried drawing right triangles but they didn't seem to work....Thanks

Let O1 & O2 be the centres of the two circles. From P draw a tangent PT meeting the second circle at T. Likewise RS//PT is tangent to the first circle. From rt. triangle PTO2, sin(TPO2)= TO2/PO2 = 1/3. The distance between RS & PT = PR*sin(TPO2)= 4*1/3 = 4/3

Thanks a lot!!!