Question

A pole stand vertically, inside a triangular park ABC.If the angle of elevation of the top of the pole from each of the corner of the park is same, then the foot of the pole is at the:
A) Centroid
B) Circumcenter
C) Incenter
D) Orthocenter

Answer 1

Hint:
A pole which is equidistant from all three corners of the triangle is called incentre, according to the question, angle of elevation is the same from all three points of the corner, which is the same, so the point is called incenter.

Complete step by step solution:
Before going into the solution lets understand, what the question is about

Where R is equidistant from pole to three corners of the triangle, and H is the height of the pole.
Now, lets understand what the options are about
Centroid: when the medians of a triangle meet at a point then the point is called centroid (a median divides the triangle into 2 equal halves)
Circumcenter: When the perpendicular bisector of the triangle meets at a point then the point is called circumcenter.
Incenter: When the angle bisector of the triangle meets at a point then the point is called incenter.
Orthocenter: When the altitudes of the triangle meet at a point then the point is called orthocenter (Altitude is perpendicular drawn from the corner of the triangle)

So, as per the question the foot of the pole is at the incenter of the triangle as shown in the figure.

Note:
Before solving any geometry questions, analyze what type of center is suitable to the requirement of the questions. And perpendicular bisectors and altitude are two different concepts.