Two parallel chords are drawn in a circle of Diameter 30 cm. The length of one chord is 24 cm and the distance between the two chords is 21 cm, find the length of other two chords.
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Answers
two parallel chords are drawn in a circle of diameter 30 cm
=> Radius = 15 cm
Distance between Chords are 21 cm
Distance between Chords 21 > 15 (Radius)
=> Chords are on different sides of a partcular diameter
Let say Perpendicular distance of chord of 24 cm length from center = x
then Perpendicular distance of other chord = 21 - x
Perpendicular from center at chord bisect the chord
=> 15² - (24/2)² = x²
=> 225 - 144 = x²
=> 81 = x²
=> x = 9
21 - x = 21 - 9 = 12
=> 15² - 12² = (Other Chord/2)²
=> 225 - 144 = (Other Chord/2)²
=> 81 = (Other Chord/2)²
=> 9 = Other Chord/2
=> Other Chord = 18 cm
length of other chord = 18 cm
Given :-
- Diameter of circle = 30 cm.
- Length of one chord = 24 cm.
- Distance between the chords = 21 cm.
To Find :-
- Length of another chord ?
Solution :-
since both chord are opposite sides of the centre .
let us assume that, distance between both chord from centre is x and y .
so,
→ x + y = distance between both chords = 21 cm.
we know that,
- perpendicular line from centre to the chord bisects the chord.
so,
→ x = √(15² - 12²) ( by pythagoras theorem)
→ x = √(225 - 144) = √81 = 9 cm.
then,
→ y = 21 - 9 = 12 cm.
therefore ,
→ Half of another chord = √(15² - 12²) = √(225 - 144) = 9 cm.
hence,
→ Total length of another chord = 9 * 2 = 18 cm. (Ans.)
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