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Circle question

2023 · Shift 2 · Q30

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PYQ Library
JEE Advanced
Mathematics
Circle
2023 · Shift 2 · Q30

Circle question

2023 · Shift 2 · Q30

JEE AdvancedMathematicsCircleNumerical+4 / −1

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 \lt r \lt 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 :

Numerical answer

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