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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:

 

(iii) (a) If arc IZA subtends an angle of 260° at the centre of the circle, then find ∠IPA
1 70°  
2 60°  
3 80°  
4 40°  

Ans.

(3)

Given, reflex ∠IOA = 260°

∠IOA=360°-260°=100°

The angle between two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

∠IPA+∠IOA=180°∠IPA+100°=180°∠IPA=180°-100°=80°