Two circles have radii of 27 cm and 36 cm. The distance between their centres is 45 cm. What is the length (in cm) of their common chord?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 43.2 cm.
Given,
Radius1, r1 = 27 cm
Radius2, r2 = 36 cm
Distance between the centers, d = 45 cm
We know,
Length of the common chord = 2 × √(4r12d2 - (r12 - r22 + d2)2)/4d2
Now,
⇒ 2 × √(4 × 272 × 45 - (272 - 362 + 452)2)/4 × 452
⇒ 2 × √(3779136/8100)
⇒ 2 × √466.56
⇒ 2 × 21.6 = 43.2 cm