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Question
Read the following passage:
People of a circular village Dharamkot want to construct a road nearest to it. The road cannot pass through the village. But the people want the road at a shortest distance from the centre of the village. Suppose the road starts from A which is outside the circular village (as shown in the figure) and touch the boundary of the circular village at B such that AB = 20 m. Also the distance of the point A from the centre O of the village is 25 m. |
Based on the above information, answer the following questions:
- If B is the mid-point of AC, then find the distance AC.
- Find the shortest distance of the road from the centre of the village.
- Find the circumference of the village.
OR
Find the area of the village.
Solution
i. B is the mid-point of AC
∴ AC = 2AB
AC = 2 × 20 = 40 m
ii. Shortest distance of the road from the centre of circle = Radius of circle
In ΔOAB, ∠B = 90°
∴ OB2 + AB2 = OA2
OB2 + 202 = 252
OB2 = 625 – 400
OB = `sqrt(225)` = 15
∴ Shortest distance = 15 m
iii. Circumference of the village
= 2πr
= `2 xx 22/7 xx 15`
= `660/7`
= `94 2/7 "m"`
OR
iii. Area of the village
= πr2
= `22/7 xx 15 xx 15`
= `4950/7`
= `707 1/7 "m"^2`
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