Let a triangle ABC be inscribed in the circle
\(x² - \sqrt2(x+y)+y² = 0\)
such that ∠BAC= π/2. If the length of side AB is √2, then the area of the ΔABC is equal to :
Let a triangle ABC be inscribed in the circle
\(x² - \sqrt2(x+y)+y² = 0\)
such that ∠BAC= π/2. If the length of side AB is √2, then the area of the ΔABC is equal to :
\(\frac{(\sqrt2+\sqrt6)}{3}\)
\(\frac{(\sqrt6+\sqrt3)}{2}\)
\(\frac{(3+\sqrt3)}{4}\)
\(\frac{(\sqrt6+2\sqrt3)}{4}\)
The Correct Option is A
Solution and Explanation
The correct answer is 1 , not there in the options
\(x² -\sqrt2(x+y)+y²=0\)
∴ Coordinates of centre of circle is \(( \frac{1}{\sqrt2} \frac{1}{\sqrt2} )\)
\(r = \sqrt{\frac{1}{2} + \frac{1}{2} - 0}\)
r = 1
BC = 2
Apply Pythagoras theorem in ΔABC, we get
AC² + AB² = BC²
⇒ AC² = 4-2 = 2
\(⇒ AC = \sqrt2\)
\(∴\) Area of ΔABC = \(\frac{1}{2}\) × AB × AC
\(\frac{1}{2} × \sqrt2 × \sqrt2 = \frac{2}{2} = 1 \) sq. unit
Top JEE Main Mathematics Questions
- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
- If , then the general value of is:
- The general solution of
- If the constant term in the binomial expansion of $\left(\frac{x^{\frac{3}{2}}}{2}-\frac{4}{x^l}\right)^9$ is $-84$ and the coefficient of $x^{-3 l}$ is $2^\alpha \beta$, where $\beta<0$ is an odd number, then $|\alpha l-\beta|$ is equal to_____
Top JEE Main Area under Simple Curves Questions
- \(f(y - 2)^2 = (x - 1)\) and \(x - 2y + 4 = 0\) then find the area bounded by the curves between the coordinate axis in first quadrant (in sq. units).
- Area bounded by \(0 ≤ y ≤ \text {min}(x^2+ 2, 2x + 2)\), \(x∈[0, 3]\), then \(12A\) is
- Let the area of the region \( \{(x, y): 0 \leq x \leq 3, 0 \leq y \leq \min\{x^2 + 2, 2x + 2\}\} \) be \( A \). Then \( 12A \) is equal to ______.
- The area enclosed by the curves xy + 4y = 16 and x + y = 6 is equal to :
- Area under the curve \(x^2 + y^2 = 169\) and below the line \(5x - y = 13\) is:
Top JEE Main Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
Concepts Used:
Area under Simple Curves
- The area of the region bounded by the curve y = f (x), x-axis and the lines x = a and x = b (b > a) - given by the formula:
- The area of the region bounded by the curve x = φ (y), y-axis and the lines y = c, y = d - given by the formula:
Read More: Area under the curve formula