Question

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

विकल्प

• centroid

• circumcentre

• incentre

• orthocentre

Answer 1

circumcentre

Explanation:

Let OP = Pole, ∠PAO = ∠PBO = ∠PCO = `alpha`

In ΔOPB, `(OP)/(OB) = tan alpha`

⇒ OB = OP cot `alpha`  ......(i)

Similarly, OA = OP cot `alpha`  ......(ii)

And OC = OP cot `alpha`  ......(iii)

From equations (i), (ii) and (iii)

OA = OB = OC ⇒ O is the point of circumcentre of the triangle ABC.