CDS Model Paper 1 Mathematics

Let the two circles with centre A, B and radii 25‌cm and 9‌cm touch each other externally at point C.
Then AB=AC+CB=25+9=34‌cm.
Let PQ the direct common tangent. i.e., BQ‌┴‌PQ and AP‌┴‌PQ. Draw BR‌┴‌AP. Then BRQP is a rctangle.
(Tangent ┴ radius at point of contact)
In Δ‌ABR,
AB2=AR2+BR2
(34)2=(16)2+(BR)2
BR2=1156−256=900
BR=√900=30‌cm
Alternatively:
Length of common tangent
√4r1r2=√4×25×9=30