Given below are two statements:
Statement I: In $$\triangle ABC$$, $$AB=6\sqrt{3}cm$$, $$AC=12cm$$ and $$BC=6cm$$, then angle $$B=90^{o}$$
Statement II: In $$\triangle ABC$$, is an isosceles with $$AC = BC$$. If $$AB^{2}= 2AC^{2}$$, then angle $$C=90^{o}$$
In the light of the above statement, choose the correct answer form the question below.

Solution

Statement I
$$AB^2+BC^2=(6\sqrt{3})^2+6^2=108+36=144$$
$$AC^2=12^2=144$$
$$AB^2+BC^2=AC^2$$
ABC is a right-angled triangle, with a right angle at B.
Statement I is true.

Statement II
$$AC^2+BC^2=AC^2+AC^2=2AC^2$$
It is given that $$AB^2=2AC^2$$
$$AB^2=AC^2+BC^2$$
ABC is a right-angled triangle, right-angled at C
Statement II is true