1

JEE Advanced 2023 Paper 2 Online

Numerical

+4

-0

Let $A_1, A_2, A_3, \ldots, A_8$ be the vertices of a regular octagon that lie on a circle of radius 2 . Let $P$ be a point on the circle and let $P A_i$ denote the distance between the points $P$ and $A_i$ for $i=1,2, \ldots, 8$. If $P$ varies over the circle, then the maximum value of the product $P A_1 \times P A_2 \times \cdots \cdots \times P A_8$, is :

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2

JEE Advanced 2023 Paper 2 Online

Numerical

+4

-0

Let $C_1$ be the circle of radius 1 with center at the origin. Let $C_2$ be the circle of radius $r$ with center at the point $A=(4,1)$, where $1 < r < 3$. Two distinct common tangents $P Q$ and $S T$ of $C_1$ and $C_2$ are drawn. The tangent $P Q$ touches $C_1$ at $P$ and $C_2$ at $Q$. The tangent $S T$ touches $C_1$ at $S$ and $C_2$ at $T$. Mid points of the line segments $P Q$ and $S T$ are joined to form a line which meets the $x$-axis at a point $B$. If $A B=\sqrt{5}$, then the value of $r^2$ is :

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3

JEE Advanced 2022 Paper 1 Online

Numerical

+3

-0

Let $$A B C$$ be the triangle with $$A B=1, A C=3$$ and $$\angle B A C=\frac{\pi}{2}$$. If a circle of radius $$r>0$$ touches the sides $$A B, A C$$ and also touches internally the circumcircle of the triangle $$A B C$$, then the value of $$r$$ is __________ .

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4

JEE Advanced 2021 Paper 2 Online

Numerical

+2

-0

Consider the region R = {(x, y) $$\in$$ R $$\times$$ R : x $$\ge$$ 0 and y

The radius of the circle C is ___________.

^{2}$$\le$$ 4 $$-$$ x}. Let F be the family of all circles that are contained in R and have centers on the x-axis. Let C be the circle that has largest radius among the circles in F. Let ($$\alpha$$, $$\beta$$) be a point where the circle C meets the curve y^{2}= 4 $$-$$ x.The radius of the circle C is ___________.

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Questions Asked from Circle (Numerical)

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