Two circles of unequal radii have four common tangents. A transverse common tangent meets the direct common tangents at the points P & Q. If length of direct common tangent (between the points of contact with the circles) is 8 then length of PQ is

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answer is 8.

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Detailed Solution

PA=PR=8−aQR=QC=b So, PQ=PR+QR=8−a+bAls_QD=QR=8−bPS=PA=a So QP=QS+SP=8−b+a8−a+b=8−b+a⇒a=bPQ=8