Two parallel chords of length 5 units and 8 units are on opposite sides of the center of a circle of radius 7 units. What is the distance between the chords? (round your answer to two decimal places)
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 12.28 units
The length of two parallel chords is 5 units and 8 units.
OM and ON are perpendicular to the chords AB and CD, respectively.
Here, AB = 5 units
So, AM = 1/2 × 5 = 2.5 units
⇒ OM2 = 72 - AM2
⇒ OM = √(72 - 2.52) = √(49 - 6.25) = √42.75 = 6.54 units
Also, CD = 8 units
So, CN = 1/2 × 8 = 4 units
⇒ ON = 72 - CN2
⇒ ON = √(72 - 42) = √(49 - 16) = √33 = 5.74 units
Distance = OM + ON = 6.54 + 5.74 = 12.28 units
Therefore, the distance between the chords is 12.28 units.