A pole stands vertically , inside a triangular park `triangle`ABC. If the angle of elevation of the top of the pole from each corner of the park is same, then in `triangle` ABC the foot of the pole is at the

Options

A. centroid
B. circumcentre
C. incentre
D. orthocentre

Answer

B

Explanation

Let OP be the pole and the angle of elevation of the top of the pole at each of the vertices A,B,C of `triangleABC` be `alpha`.
In `triangleOAP`, we have
`tan alpha =(OP)/(OA) rArr OA =OP cot alpha `

Similarly , we have
OB =OP cot `alpha` and OC =OP cot `alpha`
`therefore` OA=OB=OC.
Hence , the point O is the circumcentre of `triangleABC`.