Question 142

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

Solution

OD is the vertical pole

Hence $$\angle$$DOA = $$\angle$$DOB = 90

It is given that $$\angle$$OAD = $$\angle$$OBD

OD is common to both triangle AOD and BOD

=> $$\triangle$$AOD $$\cong$$ $$\triangle$$BOD

=> OA = OB

Similarly, OA = OC

Thus, O is equidistant from A,B and C and hence it is circumcentre.

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