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Mathematics - Circle Question with Solution | TestHub

MathematicsCircleEquation of chord with given middle point Chord of contact Pair of TangentsMedium2 minQB

MathematicsMediumsingle choice

$A B$ is a chord of $x^{2} + y^{2} = 25$ . Tangents at $A, B$ meet at $C$ . If $(2, 3)$ is the midpoint of $A B$ , find the area of $O A CB$ .

Options:

Answer:

Solution:

The midpoint is at distance $13$ from $O$ ; half the chord length is $25 - 13 = 23$ . The tangent intersection has $OC = 25/ 13$ . Thus the quadrilateral area is $\frac{1}{2} (43) (25/ 13) = 50 3/13$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Equation of chord with given middle point Chord of contact Pair of Tangents

⏱ 2mℹ️ Source: QB

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