Two circles of radii 8 cm and 5 cm with their centres A and B respectively touch externally as shown in the figure. Calculate the length of direct common tangent PQ

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Solution

Draw a line parallel to PQ from point B such that it cuts AP at M.

It is given that AP = 8 cm and BQ = 5 cm.

Here, we need to find the length of PQ.

AM = AP – PM = AP – BQ = 8 cm – 5 cm = 3 cm

Since the two circles touch each other externally, the distance between their centers is equal to sum of their radii.

AB = 8 cm + 5 cm = 13 cm

Applying Pythagoras theorem in right ΔMAB, we have:

PQ = BM = 12.64

Hence, the length of the common tangent is 12.64 cm.

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