Question
Download Solution PDFTwo 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)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Two parallel chords of length 5 units and 8 units are on opposite sides of the center of a circle of radius 7 units.
We need to find the distance between the chords.
Formula used:
In a right triangle:
OM = √(r² - AM²), where OM is the perpendicular distance from the center to the chord.
Calculation:
For the chord of length 5 units:
⇒ AM = 1/2 × 5 = 2.5 units
⇒ OM² = r² - AM²
⇒ OM = √(7² - 2.5²)
⇒ OM = √(49 - 6.25)
⇒ OM = √42.75 = 6.54 units
For the chord of length 8 units:
⇒ CN = 1/2 × 8 = 4 units
⇒ ON² = r² - CN²
⇒ ON = √(7² - 4²)
⇒ ON = √(49 - 16)
⇒ ON = √33 = 5.74 units
Therefore, the distance between the chords:
⇒ Distance = OM + ON
⇒ Distance = 6.54 + 5.74 = 12.28 units
∴ The distance between the chords is 12.28 units.
Last updated on May 28, 2025
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