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Intersection between Tangent and Secant

A red and blu...

Question

A red and blue cardboard discus of radii 4.5 cm and 2 cm are fixed to a straight string of length 10 cm; as shown in the figure. What is the radius of another disc, which touches the circular discs at P and Q.

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Solution

The given figure is:

It is given that AB = 10 cm, AP = 4. 5 cm and BQ = 2 cm.

Now, PQ = 10 cm – 4.5 cm – 2 cm = 3.5 cm

Radius of the disc, which touches both discs at P and Q = = 1.75 cm

Hence, the radius of the circular disc that touches the other two discs is 1.75 cm.

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