JEE PYQ: Circle Question 32
Question 32 - 2019 (12 Apr Shift 1)
If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is $90°$, then the length (in cm) of their common chord is:
(1) $\frac{13}{5}$
(2) $\frac{120}{13}$
(3) $\frac{60}{13}$
(4) $\frac{13}{2}$
Show Answer
Answer: (2)
Solution
At right angle intersection: $d^2 = r_1^2 + r_2^2 = 25 + 144 = 169$, $d = 13$. Common chord $= \frac{2r_1 r_2}{d} = \frac{2 \times 5 \times 12}{13} = \frac{120}{13}$.
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