O is the centre of the given circle. A tangent PR has been drawn touching the circle at point P. Draw QP ⊥ RP at point P, such that point Q lies on the circle. ∠OPR = 90° (radius ⊥ tangent) Also, ∠QPR = 90° (Given) ∴ ∠OPR = ∠QPR Now, above case is possible only when centre O lies on the line QP. Hence, perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.
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Solution: Area of the valley, A = 97280 km2
Level in the rise of water in the valley, h = 10 cm = (10/100000) km = (1/10000) km Thus, amount of rain fall in 14 day = Ah = 97280 km2 × (1/10000) km = 9.828 km3 Amount of rain fall in 1 day = 9.828 /14 = 0.702km3 Volume of water in 3 rivers = length × breadth × height = 1072 km × 75 m × 3 m = 1072 km × (75/1000) km × (3/1000) km = 0.2412 km3 x3 = 0.7236 km3 This shows that the amount of rain fall is approximately equal to the amount of water in three rivers. Optional Exercise – 13.5 - 10th Mathematics –Surface area and Volume |