Question:
\(AB\) is a diameter of a circle and \(C\) is any point on the circumference of the circle. Then
\(AB\) is a diameter of a circle and \(C\) is any point on the circumference of the circle. Then
Show Hint
Angle in semicircle is \(90^\circ\). Area = \(\frac{1}{2} \times \text{base} \times \text{height}\).
Updated On: Apr 23, 2026
- The area of \(\Delta ABC\) is maximum when it is isosceles
- The area of \(\Delta ABC\) is minimum when it is isosceles
- The perimeter of \(\Delta ABC\) is minimum when it is isosceles
- None of these
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Formula / Definition}
\[ \text{Area} = \frac{1}{2} \cdot AB \cdot h \]
Step 2: Calculation / Simplification}
\(AB = d\) (constant). Height \(h = AC \sin \angle CAB\)
Maximum area when \(h\) is maximum
\(h\) maximum when \(C\) is at highest point (perpendicular to \(AB\))
At this point, \(AC = BC \Rightarrow\) isosceles right triangle.
Step 3: Final Answer
\[ \text{The area of } \Delta ABC \text{ is maximum when it is isosceles} \]
\[ \text{Area} = \frac{1}{2} \cdot AB \cdot h \]
Step 2: Calculation / Simplification}
\(AB = d\) (constant). Height \(h = AC \sin \angle CAB\)
Maximum area when \(h\) is maximum
\(h\) maximum when \(C\) is at highest point (perpendicular to \(AB\))
At this point, \(AC = BC \Rightarrow\) isosceles right triangle.
Step 3: Final Answer
\[ \text{The area of } \Delta ABC \text{ is maximum when it is isosceles} \]
Was this answer helpful?
0
0
Top MET Mathematics Questions
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- The equation $3^{3x + 4} = 9^{2x - 2},\ x>0$ has the solution
- A parallelogram is constructed on the vectors $\mathbf{a} = 3\alpha - \beta$, $\mathbf{b} = \alpha + 3\beta$. If $|\alpha| = |\beta| = 2$ and the angle between $\alpha$ and $\beta$ is $\dfrac{\pi}{3}$, then the length of a diagonal of the parallelogram is
- Every group of order 7 is
- Let $U_{n} = 2 + 2^{3} + 2^{5} + \cdots + 2^{2n+1}$ and $V_{n} = 1 + 4 + 4^{2} + \cdots + 4^{n-1}$. Then $\displaystyle\lim_{n \to \infty} \dfrac{U_n}{V_n}$ is equal to
View More Questions
Top MET Trigonometry Questions
- If $\tan^{-1}x + \tan^{-1}y + \tan^{-1}z = \pi$, then $x + y + z$ is
- If $3\sin^{-1}\!\left(\dfrac{2x}{1+x^{2}}\right) - 4\cos^{-1}\!\left(\dfrac{1-x^{2}}{1+x^{2}}\right) + 2\tan^{-1}\!\left(\dfrac{2x}{1-x^{2}}\right) = \dfrac{\pi}{3}$, then $x$ equals
- If $\sin(\pi \cos \theta) = \cos(\pi \sin \theta)$, then which of the following is correct?
- $\sin^{-1}\dfrac{1}{\sqrt{5}} + \cos^{-1}\dfrac{3}{\sqrt{10}}$ is equal to
- If $4\sin^{-1}x + \cos^{-1}x = \pi$, then $x$ is equal to
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions