Question:
Let A(α, -2), B(α, 6) and C(\(\frac{\alpha}{4}\), -2) be vertices of a ΔABC. If (5, \(\frac{\alpha}{4}\)) is the circumcentre of ΔABC, then which of the following is NOT correct about ΔABC?
Let A(α, -2), B(α, 6) and C(\(\frac{\alpha}{4}\), -2) be vertices of a ΔABC. If (5, \(\frac{\alpha}{4}\)) is the circumcentre of ΔABC, then which of the following is NOT correct about ΔABC?
Updated On: Dec 18, 2024
- Area is 24
- Perimeter is 25
- Circumradius is 5
- Inradius is 2
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Circumcentre of ΔABC
=(\(\alpha+\frac{\frac{\alpha}{4}}{2}\),\(\frac{6-2}{2}\))
=(\(\frac{5\alpha}{8}\), 2)
=(5,\(\frac{\alpha}{4}\))
⇒α=8
Area (ΔABC)=\(\frac{1}{2}\)⋅3α4×8=24 sq. units
Perimeter =8+\(\frac{3\alpha}{4}\)+\(\sqrt{82}\)+(\(\frac{3\alpha}{4}^2\))
=8+6+10=24
Circumradius=\(\frac{10}{2}\)=5
r=\(\frac{\Delta}{s}\)
r=\(\frac{24}{12}\)
r=2
So, the correct option is (B): Perimeter is 25.
=(\(\alpha+\frac{\frac{\alpha}{4}}{2}\),\(\frac{6-2}{2}\))
=(\(\frac{5\alpha}{8}\), 2)
=(5,\(\frac{\alpha}{4}\))
⇒α=8
Area (ΔABC)=\(\frac{1}{2}\)⋅3α4×8=24 sq. units
Perimeter =8+\(\frac{3\alpha}{4}\)+\(\sqrt{82}\)+(\(\frac{3\alpha}{4}^2\))
=8+6+10=24
Circumradius=\(\frac{10}{2}\)=5
r=\(\frac{\Delta}{s}\)
r=\(\frac{24}{12}\)
r=2
So, the correct option is (B): Perimeter is 25.
Was this answer helpful?
0
1
Top Questions on Horizontal and vertical lines
- Let \(\alpha, \beta, \gamma\) be the foot of perpendicular from the point \((1, 2, 3)\) on the line \(\frac{x + 3}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}\). Then \(19(\alpha + \beta + \gamma)\) is equal to:
- JEE Main - 2024
- Mathematics
- Horizontal and vertical lines
- Let \((\alpha, \beta, y)\) be the foot of perpendicular form the point \((1,2,3)\) on the line \(\bigg(\frac{x + 3}{5}\) = \(\frac{y - 1}{2}\) = \(\frac{z + 4}{3}\) \(\bigg)\)then \(19 (\alpha + \beta + y)\)
- JEE Main - 2024
- Mathematics
- Horizontal and vertical lines
- If $4a^2 + b^2 + 2c^2 + 4ab - 6ac - 3bc = 0$, the family of lines $ax + by + c = 0$ is concurrent at one or the other of the two points-
- BITSAT - 2013
- Mathematics
- Horizontal and vertical lines
- The distance between the parallel lines $ y=x+a,\,\,y=x+b $ is
- JKCET - 2008
- Mathematics
- Horizontal and vertical lines
- A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2 + y^2 = 4$ with $x + y = a$. The set containing the value of '$a$' is
- BITSAT - 2008
- Mathematics
- Horizontal and vertical lines
View More Questions
Questions Asked in JEE Main exam
- For a sparingly soluble salt \( \text{AB}_2 \), the equilibrium concentrations of \( \text{A}^{2+} \) ions and \( \text{B}^- \) ions are \( 1.2 \times 10^{-4} \, \text{M} \) and \( 0.24 \times 10^{-3} \, \text{M} \), respectively. The solubility product of \( \text{AB}_2 \) is:
- JEE Main - 2024
- Method of Preparation of Diazoniun Salts
The portion of the line \( 4x + 5y = 20 \) in the first quadrant is trisected by the lines \( L_1 \) and \( L_2 \) passing through the origin. The tangent of an angle between the lines \( L_1 \) and \( L_2 \) is:
- JEE Main - 2024
- Tangents and Normals
- Let \[ \vec{a} = 2\hat{i} + \alpha \hat{j} + \hat{k}, \quad \vec{b} = -\hat{i} + \hat{k}, \quad \vec{c} = \beta \hat{j} - \hat{k}, \] where \( \alpha \) and \( \beta \) are integers and \( \alpha \beta = -6 \). Let the values of the ordered pair \( (\alpha, \beta) \) for which the area of the parallelogram of diagonals \( \vec{a} + \vec{b} \) and \( \vec{b} + \vec{c} \) is \( \frac{\sqrt{21}}{2} \), be \( (\alpha_1, \beta_1) \) and \( (\alpha_2, \beta_2) \). Then \( \alpha_1^2 + \beta_1^2 - \alpha_2 \beta_2 \) is equal to:
- JEE Main - 2024
- Vectors
- The molecular formula of second homologue in the homologous series of monocarboxylic acid is
- JEE Main - 2024
- Aldehydes, Ketones and Carboxylic Acids
- Given below are two statements: Statement I: $\text{PF}_5$ and $\text{BrF}_5$ both exhibit $\text{sp}^3\text{d}$ hybridisation.Statement II: Both $\text{SF}_6$ and $[\text{Co}(\text{NH}_3)_6]^{3+}$ exhibit $\text{sp}^3\text{d}^2$ hybridisation. In the light of the above statements,choose the correct answer from the options given below:
- JEE Main - 2024
- Hybridisation
View More Questions
Concepts Used:
Horizontal and vertical lines
Horizontal Lines:
- A horizontal line is a sleeping line that means "side-to-side".
- These are the lines drawn from left to right or right to left and are parallel to the x-axis.
Equation of the horizontal line:
In all cases, horizontal lines remain parallel to the x-axis. It never intersects the x-axis but only intersects the y-axis. The value of x can change, but y always tends to be constant for horizontal lines.
Vertical Lines:
- A vertical line is a standing line that means "up-to-down".
- These are the lines drawn up and down and are parallel to the y-axis.
Equation of vertical Lines:
The equation for the vertical line is represented as x=a,
Here, ‘a’ is the point where this line intersects the x-axis.
x is the respective coordinates of any point lying on the line, this represents that the equation is not dependent on y.
⇒ Horizontal lines and vertical lines are perpendicular to each other.