Manipal MET2013MathematicsProperties of Triangles
In an equilateral triangle, the in-radius, circum-radius and one of the ex-radii are in the ratio
Options
- A2: 3: 5
- B1: 2: 3
- C1: 3: 7
- D3: 7: 9
Correct answer
B. 1: 2: 3
Step-by-step solution
We have; = 3 4 a^2, s= 3 a 2 r= S = a 2 3 , R= a b c 4 = a^3 3 a^2 = a 3 and r₁= S-a = 3 / 4 a^2 a / 2 = 3 2 a Hence; r: R: r₁= a 2 3 : a 3 : 3 2 a=1: 2: 3