New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Circle question

2024 · 6 Apr · Shift 1 · Q31

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Circle
2024 · 6 Apr · Shift 1 · Q31

Circle question

2024 · 6 Apr · Shift 1 · Q31

JEE MainMathematicsCircleMCQ+4 / −1

A circle is inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed in this circle are

m

and

n

, respectively, then

m+n^2

is equal to

A
408
B
414
C
312
D
396

More from Circle

If $P (6, 1)$ be the orthocentre of the triangle whose vertices are $A (5, - 2), B (8, 3)$ and $C (h, k)$ , then the point $C$ lies on the circle :2024 · MCQ
Let the circles $C_{1} : (x - α)^{2} + (y - β)^{2} = r_{1}^{2}$ and $C_{2} : (x - 8)^{2} + (y - \frac{15}{2})^{2} = r_{2}^{2}$ touch each other externally at the point $(6, 6)$ . If the point $(6, 6)$ divides the line segment joining the centres of the circles…2024 · MCQ
If the image of the point $(- 4, 5)$ in the line $x + 2 y = 2$ lies on the circle $(x + 4)^{2} + (y - 3)^{2} = r^{2}$ , then $r$ is equal to:2024 · MCQ
Let a circle passing through $(h, k)$ have its centre at the point $(x_{c}, y_{c})$ . Let $(x_{c}, y_{c})$ be the point of intersection of the lines $3 x + 5 y = 1$ and $(2 + c) x + 5 c^{2} y = 1$ . If $h = lim_{c \to 1} x_{c}$ …2024 · MCQ
Let the centre of a circle, passing through the points $(0, 0), (1, 0)$ and touching the circle $x^{2} + y^{2} = 9$ , be $(h, k), 4 (h^{2} + k^{2})$ . Then for all possible values of the coordinates of the centre $(h, k), 4 (h^{2} + k^{2})$ is equal to …2024 · Numerical
Four distinct points $(2 k, 3 k), (1, 0), (0, 1)$ and $k$ lie on a circle for $k$ equal to :2024 · MCQ
Consider a circle $(x - α)^{2} + (y - β)^{2} = 50$ , where $α, β > 0$ . If the circle touches the line $y + x = 0$ at the point $P$ , whose distance from the origin is $42$ , then $(α + β)^{2}$ is equal to …2024 · Numerical
Equations of two diameters of a circle are $2 x - 3 y = 5$ and $3 x - 4 y = 7$ . The line joining the points $(- \frac{22}{7}, - 4)$ and $(- \frac{1}{7}, 3)$ intersects the circle at only one point $P (α, β)$ . Then, $17 β - α$ …2024 · Numerical