An equilateral triangle $A B C$ is inscribed in a circle of radius $20 \sqrt{3} \mathrm{~cm}$. The centroid of the triangle $A B C$ is at a distance $d$ from the vertex $A$. then $d$ is equal to ?

Given below are two statements:

Statement I: In $\triangle A B C, A B=6 \sqrt{3} \mathrm{~cm}, A C=12 \mathrm{~cm}$ and $B C=6 \mathrm{~cm}$, then angle $B=90^{\circ}$

Statement II: In $\triangle A B C$, is an isosceles with $A C=B C$. If $A B^{2}=2 AC^{2}$, Then angle $C=90^{\circ}$

In the light of the above statement, choose the correct answer form the question below.

ABC is right angled triangle at C. Let BC = a, CA = b and AB = c and let p be the length of perpendicular from C on AB, then cp is equal to

An equilateral triangle $\mathrm{ABC}$ is inscribed in a circle of radius $20 \sqrt{3} \mathrm{~cm}$. What is the length of the side of the triangle ?

The sides of four triangles are given below. Which of them forms a right triangle ?

(A) $20 \mathrm{~cm}, 22 \mathrm{~cm}, 24 \mathrm{~cm}$

(B) $15 \mathrm{~cm}, 32 \mathrm{~cm}, 37 \mathrm{~cm}$

(C) $11 \mathrm{~cm}, 60 \mathrm{~cm}, 61 \mathrm{~cm}$

(D) $6 \mathrm{~cm}, 8 \mathrm{~cm}, 10 \mathrm{~cm}$

The points $(2,2),(6,3)$ and $(4,11)$ are vertices of :