Properties of Triangles · Mathematics · NDA
MCQ (Single Correct Answer)
Statement I
If the line segment joining the points P(m, n) and Q(r, s) subtends an angle $$\alpha$$ at the origin, then $$\cos \alpha = {{ms - nr} \over {\sqrt {({m^2} + {n^2})({r^2} + {s^2})} }}$$.
Statement II
In any triangle ABC, it is true that $${a^2} = {b^2} + {c^2} - 2bc\cos A$$.
Which one of the following is correct in respect of the above two statements?
In a triangle ABC, ∠A = 75° and ∠B = 45°. What is 2a - b equal to?
$ABC$ is a triangle such that angle $C = 60^{\circ}$, then what is $\frac{\cos A + \cos B}{\cos \left(\frac{A - B}{2}\right)}$ equal to?
In a triangle $ABC$, $AB=16 \text{ cm}, BC=63 \text{ cm}$ and $AC=65 \text{ cm}$. What is the value of $\cos 2A+\cos 2B+\cos 2C$?
Consider the following statements:
1. In a triangle $ABC$, if $\cot A \cdot \cot B \cdot \cot C>0$, then the triangle is an acute-angled triangle.
2. In a triangle $ABC$, if $\tan A \cdot \tan B \cdot \tan C > 0$, then the triangle is an obtuse-angled triangle.
Which of the statements given above is/are correct?
Consider the following statements :
1. ABC is right angled triangle
2. The angles of the triangle are in AP
Which of the statements given above is/are correct ?
What is $\frac{\text{AB}}{\sin \text{C}}$ equal to ?
What is cos A + cos B + cos C equal to ?
Consider the following statements:
1. The third vertex has at least one irrational coordinate.
2. The area is irrational.
Which of the above statements is/are correct?