Question:
In a triangle ABC, $r_1 \cot \dfrac{A}{2} + r_2 \cot \dfrac{B}{2} + r_3 \cot \dfrac{C}{2} = $ ?
In a triangle ABC, $r_1 \cot \dfrac{A}{2} + r_2 \cot \dfrac{B}{2} + r_3 \cot \dfrac{C}{2} = $ ?
Show Hint
Each $r_i \cot\left(\dfrac{\text{angle}}{2}\right) = s$ in a triangle; so the sum over all three equals $3s$.
Updated On: May 18, 2025
- $s$
- $2s$
- $3s$
- $\dfrac{s}{2}$
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Using the identity:
\[
r_a \cot\left(\frac{A}{2}\right) = s,\quad r_b \cot\left(\frac{B}{2}\right) = s,\quad r_c \cot\left(\frac{C}{2}\right) = s
\Rightarrow r_1 \cot \frac{A}{2} + r_2 \cot \frac{B}{2} + r_3 \cot \frac{C}{2} = s + s + s = 3s
\]
Was this answer helpful?
0
0
Top Questions on Triangles
- If the distance of a variable point \(P\) from a point \(A(2,-2)\) is twice the distance of \(P\) from the Y-axis, then the equation of locus of \(P\) is:
- The coordinate axes are rotated about the origin in the counterclockwise direction through an angle \( 60^\circ \). If \( a \) and \( b \) are the intercepts made on the new axes by a straight line whose equation referred to the original axes is \( x + y = 1 \), then \( \dfrac{1}{a^2} + \dfrac{1}{b^2} = \, ? \)
- The image of a point \( (2, -1) \) with respect to the line \( x - y + 1 = 0 \) is
- If \( \sinh^{-1}(2) + \sinh^{-1}(3) = \alpha \), then \( \sinh\alpha = \) ?
- If in \( \triangle ABC \), \( B = 45^\circ \), \( a = 2(\sqrt{3} + 1) \) and area of \( \triangle ABC \) is \( 6 + 2\sqrt{3} \) sq. units, then the side \( b = \ ? \)
View More Questions
Questions Asked in AP EAPCET exam
- In a container of volume 16.62 m$^3$ at 0°C temperature, 2 moles of oxygen, 5 moles of nitrogen and 3 moles of hydrogen are present, then the pressure in the container is (Universal gas constant = 8.31 J/mol K)
- AP EAPCET - 2025
- Ideal gas equation
- If \[ A = \begin{bmatrix} x & 2 & 1 \\ -2 & y & 0 \\ 2 & 0 & -1 \end{bmatrix}, \] where \( x \) and \( y \) are non-zero real numbers, trace of \( A = 0 \), and determinant of \( A = -6 \), then the minor of the element 1 of \( A \) is:}
- AP EAPCET - 2025
- Complex numbers
- Two objects of masses 5 kg and 10 kg are placed 2 meters apart. What is the gravitational force between them?
(Use \(G = 6.67 \times 10^{-11}\, \mathrm{Nm^2/kg^2}\))- AP EAPCET - 2025
- Gravitation
- The number of solutions of the equation $4 \cos 2\theta \cos 3\theta = \sec \theta$ in the interval $[0, 2\pi]$ is
- AP EAPCET - 2025
- Trigonometric Identities
- The area (in sq. units) of the triangle formed by the tangent and normal to the ellipse \( 9x^2 + 4y^2 = 72 \) at the point (2, 3) with the X-axis is
- AP EAPCET - 2025
- Coordinate Geometry
View More Questions