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Line AB touches circle (p,12) at A and circle (Q, 5) at B. If PQ = 25 and A and B are either side of line PQ then AB=-

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I assume that "circle (P,12)" means a circle with center at P and radius 12. If so, then the distance between the circles is 25-12-5 = 8

Draw the diagram. Label O the point midway between the circles. Then we have two right triangles

PAO and QBO

PO=16 and PA=12
QO=9 and QB=5

AB=AO+OB
= √(16^2-12^2) + √(9^2-5^2)
= 4√7 + 2√14
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