Question
In a triangle 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=?
Answer: Option C
:
C
Option (c)
Let 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= √34 a2 = 3√3.
1h1=1h2=1h3=13. Sum = 1
Only option c gives 1.
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:
C
Option (c)
Let 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= √34 a2 = 3√3.
1h1=1h2=1h3=13. Sum = 1
Only option c gives 1.
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