Answer the Following:

Question

An equilateral triangle DOG, X is its orthocenter. Which statement(s) must be true? I. triangle DOG is equiangular II. X is the incenter of triangle DOG III. X is the point of concurrency of its 3 medians.

A. I only

B. I, II, and III

C. II and IiI only

D. I and III only

Answer 1

the angles are all 60 degrees or 2pi/3 radians, so "equiangular"

orthocenter is the intersection of the 3 altitudes. Use each side as a base and the altitude is the height. where the 3 heights intersect is the orthocenter. Each height = bsqr3/2. They all intersect at the same point in the center of the equilateral triangle

the incenter is the center of an inscribed circle, which is the same as the orthocenter for an equilateral triangle

the 3 medians are the same as the 3 altitudes for an equilateral triangle. they meet, intersect at the orthocenter or incenter.

Answer is I,II and III