Mathematics - Circle Question with Solution | TestHub

MathematicsCircleCommon tangents to two circlesHard2 minQB

MathematicsHardmultiple choice

Let $C_{1} = x^{2} + y^{2} = r_{1}^{2}, C_{2} = x^{2} + y^{2} = r_{2}^{2} (r_{1} < r_{2})$ be two circles. Let A be the fixed point $(r_{1}, 0)$ on $C_{1}$ and B be a variable point on $C_{2}$ . Let the line BA meet the circle $C_{2}$ again at E .

Then,

Options:(select one or more)

Answer:

A, B, C, D

Solution:

$(BE)_{max} =$ diameter of circle

$C_{2} = 2 r_{2}$ $(BE)_{min} = 2 r_{2}^{2} - r_{1}^{2}$

$(O A^{2} + O B^{2} + B E^{2})_{min}$ is, $r_{1}^{2} + r_{2}^{2} + 4 r_{2}^{2} - 4 r_{1}^{2} = 5 r_{2}^{2} - 3 r_{1}^{2}$

$(O A^{2} + O B^{2} + B E^{2})_{max}$ is , $r_{1}^{2} + r_{2}^{2} + 4 r_{2}^{2} = r_{1}^{2} + 5 r_{2}^{2}$

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Common tangents to two circles

⏱ 2mℹ️ Source: QB

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