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In the figure below, M and N are the centres of two semi-circles having radii 9 cm and 16 cm respectively.

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In the figure below, M and N are the centres of two semi-circles having radii 9 cm and 16 cm respectively. ST is a common tangent.

Find the length of PQ. Draw a rough figure, show your work and give valid reasons.

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Join MP, NQ and draw MR parallel to PQ.

RN = 16 - 9 = 7cm and 

MN = 9 + 16 = 25 CM

In triangle MRN , By Pythagoras theorem

MR = √(252 - 72)

= 24 cm

Now since MRQP is a rectangle, PQ = MR = 24 cm

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