A line cuts two concentric circles. The length of chords formed by this line on the circles is 6 cm and 18 cm. Find the difference in the squares of the radii of two circles.
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 72.
Let the radii of the smaller and bigger circles be r and R.
AB = BC/2 = 6/2 = 3 cm
AD = DE/2 = 18/2 = 9 cm
In ΔOAB, OB2 = OA2 + AB2
⇒ r2 - AB2 = OA2 ....(1)
In ΔOAC, OD2 = OA2 + AD2
⇒ R2 - AD2 = OA2 ....(2)
From equations (1) and (2),
r2 - AB2 = R2 - AD2
⇒ r2 - 32 = R2 - 92
⇒ r2 - 9 = R2 - 81
⇒ R2 - r2 = 81 - 9 = 72
Therefore, the required difference in the squares of the radii of two circles is 72 cm2.