1

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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2

JEE Advanced 2023 Paper 2 Online

Numerical

+3

-0

Consider an obtuse angled triangle $A B C$ in which the difference between the largest and the smallest angle is $\frac{\pi}{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.

$$
\text { Let } a \text { be the area of the triangle } A B C \text {. Then the value of }(64 a)^2 \text { is }
$$ :

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3

JEE Advanced 2023 Paper 2 Online

Numerical

+3

-0

Consider an obtuse angled triangle $A B C$ in which the difference between the largest and the smallest angle is $\frac{\pi}{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.

$$
\text { Then the inradius of the triangle } A B C \text { is }
$$ :

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4

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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Questions Asked from Circle (Numerical)

Number in Brackets after Paper Indicates No. of Questions

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