Question

# In triangle XYZ, r is the radius of the incircle, R is the radius of the circumcircle and A is the area of the triangle. If h1,h2 and h3 are the 3 altitudes of the triangle, then 1h1+1h2+1h3=?

A
r/A
B
1/R
C
1/r
D
R/A

Solution

## The correct option is A 1/rLet a = side, h = height, Since no conditions are mentioned and only variables are used, we can assume an equilateral triangle. Let r =1. Then R = 2., h = 3. In an equilateral triangle r : R : h = 1 : 2 : 3 Side a = 2 √3; Area= √3a24= 3√3. 1h1=1h2=1h3=13. Sum = 1 Only option c gives 1.

Suggest corrections