Question

People of village want to construct a road nearest to a circular village Rampur. The road cannot pass through the village. But the people want the road should be at the shortest distance from the centre of the village(i) If the road start from point O which is outside the circular village and touch the boundary of the circular village at pointA such that OA= 20 cm. If the straight distance of the point O from the centre C of the village is 25 cm, then find theshortest distance of the road from the centre of the village.(ii) Which method should be apply to find the shortest distance?​

Answer 1

Answer:

distance is 10km ggffddfghh

Answer 2

15 cm

The Pythagoras Theorem.

Step-by-step explanation:

See the attached diagram.

The shortest distance from the center of the village C to the road OA will be the radius CA of the circular village.

Now, assume that CA = x cm.

Here, the triangle Δ COA is a right triangle as OA is tangent to the circle and CA is the radius of it.

So, applying Pythagoras Theorem we will get,

CO² = CA² + OA²

⇒ 25² = x² + 20²

⇒ x² = 225

⇒ x = 15 cm.

Therefore, the shortest distance of the road from the center of the village is 15 cm. (Answer)

We have used the Pythagoras Theorem applicable for a right triangle that is, (Hypotenuse)² = (Base)² + (Height)² (Answer)