Question

A triangle is inscribed in a circle of radius 1. The distance between the orthocenter and the circumcenter of the triangle cannot be

Answer 1

The distance between the orthocenter and the circumcenter of the triangle cannot be greater than 3 or 4

Step-by-step explanation:

here , A triangle is inscribed in a circle of radius 1

then

we know that the

for any triangle , the inequality

HO ≤ 3 R

where  H is the orthocenter and O is the circumcenter and R is the circumradius

then

here R = 1

therefore

HO ≤ 3  

i.e The distance between the orthocenter and the circumcenter of the triangle cannot be greater than 3

so ,

The distance between the orthocenter and the circumcenter of the triangle cannot be greater than 3 or 4

#Learn more :

Distance between orthocenter and circumcenter of a triangle formula

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