Mathematics - Circle Question with Solution | TestHub

MathematicsCircleFamily of circlesMedium2 minPYQ_2019

MathematicsMediumsingle choice

If the angle of intersection at a point where the two circles with radii $5 c m$ and $12 c m$ intersect is $90 °$ , then the length (in cm) of their common chord is:

Options:

Answer:

Solution:

$∵ C_{1} P = 5$
$C_{2} P = 12 & ∠ C_{1} P C_{2} = 90^{o}$
$∴ C_{1} C_{2} = 13$
$∴ Δ C C_{2} P$
$\tan θ = \frac{12}{5} \Rightarrow \sin θ = \frac{12}{13}$
$C_{1} C_{2}$ biscets the $P Q$ at $R$ & $C_{1} C_{2} ⊥ P Q$
in $Δ P C_{1} R, s i n θ = \frac{P R}{5}$
$\Rightarrow \frac{12}{13} = \frac{P R}{5} \Rightarrow P R = \frac{60}{13}$
& $P Q = 2 P R = \frac{120}{13}$

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Family of circles

⏱ 2mℹ️ Source: PYQ_2019

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