Exam

JEE Main

Year

2019

Date

12 April

Shift

Morning Shift

Subject

Mathematics

Chapter

Circle

JEE Main 2019 · 12 April · Morning Shift · Mathematics · Circle

If the angle of intersection at a point where the two circles with...

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

Step-by-step solution

$∵ {C}_{1}P = 5$
${C}_{2}P = 12 \text{ and } ∠{C}_{1}P{C}_{2} = {90}^{o}$
$∴ {C}_{1}{C}_{2} = 13$
$∴ \DeltaC{C}_{2}P$
$tan \theta = \dfrac{12}{5} ⇒ sin \theta = \dfrac{12}{13}$
${C}_{1}{C}_{2}$ biscets the $PQ$ at $R$ & ${C}_{1}{C}_{2} ⊥ PQ$
in $\DeltaP{C}_{1}R, sin\theta = \dfrac{PR}{5}$
$⇒ \dfrac{12}{13} = \dfrac{PR}{5} ⇒ PR = \dfrac{60}{13}$
& $PQ = 2PR = \dfrac{120}{13}$