`Delta I_(1)I_(2)I_(3)` is an excentral triangle of an equilateral triangle `Delta ABC` such that `I_(1)I_(2)=4` unit, if `DeltaDEF` is pedal triangle

Correct option is (D) 60° All three angles are equal in an equilateral triangle. Also sum of all three angles in a triangle is \(180^\circ.\) \(\therefore\) One angle in equilateral triangle \(=\frac{180^\circ}3=60^\circ.\)

Correct option is  D) 2.8 cm

Correct option is  D) 120°

Correct option is  C) 15 cm

Correct option is (B) √3 cm2 Side of equilateral triangle is a = 2 cm \(\therefore\) Area of equilateral triangle \(=\frac{\sqrt3}4a^2\) \(=\frac{\sqrt3}4\times2^2\) = \(\sqrt{3}\) \(cm^2\)

Correct option is (C) 12√2 Let side of equilateral triangle is a cm. Then \(\frac{\sqrt3}4a^2=8\sqrt3\)   \((\because\) Area of equilateral triangle is \(\frac{\sqrt3}4a^2)\) \(\therefore a^2=32\) \(\Rightarrow a=\sqrt{16\times2}=4\sqrt2\) \(\therefore\) Perimeter of equilateral triangle = 3a \(=3\times4\sqrt2\) \(=12\sqrt2\,cm\)

Correct Answer - D NA

Correct Answer - A::C::D Clearly `R(alpha,beta)` is centroid of `DeltaABC`s `:.R(alpha,beta)=((3+1+2)/3,(9+2+3)/3)=(2,14/3)` `impliesalpha=2` and `beta=14/3` Hence `2alpha+3beta=18`