Question : Two circles of radii 5 cm and 3 cm touch externally. The ratio in which the direct common tangent to the circles divides externally the line joining the centres of the circles is:
Option 1: 5 : 3
Option 2: 2 : 5
Option 3: 5 : 1
Option 4: 3 : 8
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Correct Answer: 5 : 3
Solution :
Given: Two circles of radii 5 cm and 3 cm touch externally.
Let, the circle with centre A has a radius OA = 5 cm and
the circle with centre C has a radius OC = 3 cm
So, the direct common tangent to the circles divides the line joining the centres of the two circles at O.
Thus, it divides AC in the ratio of 5 : 3.
Hence, the correct answer is 5 : 3.
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