If PO = 25 cm, then find IO.

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Solution

Q.
The chain and gears of bicycles or motorcycles, as well as the belt around pulleys, are real-life examples of tangents to a circle. One such example is shown in Fig, where PI and PA represent tangents to the gears of a bicycle.

Based on the above information, answer the following questions:

(ii) If PO = 25 cm, then find IO.

1 10 cm

2 11 cm

3 14 cm

4 15 cm

Ans.
(4)

Consider Fig.

In right triangle ΔPIO, we have

$O P^{2} = P I^{2} + I O^{2} (25)^{2} = (20)^{2} + I O^{2}$

$I O^{2} = 625 - 400 = 225 I O = 15 cm$

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