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Two parallel chords are drawn on the same side othe center of circle of radius R. It is found that they subtending an angle of 2A and A at the center. Find the perpendicular distance between the chords?

Two parallel chords are drawn on the same side othe center of circle of radius R. It is found that they subtending an angle of 2A and A at the center. Find the perpendicular distance between the chords?

Grade:11

1 Answers

Sujit Kumar
111 Points
6 years ago
Sorry the last Step is wrong in the above solution. The answer is y=r(Cos\frac{A}{2}-CosA)
Let The perpendicular distance from center to side opposite to angle A be x
and the perpendicular distance from center to side opposite to angle 2A be x-y
Required to find:- The value of y
 
Applying Trigonometory,
 
On triangle with angle A
Cos\frac{A}{2}= \frac{x}{r}=>x=r(Cos\frac{A}{2})__________(1)
 
On triangle with angle 2A
CosA= \frac{x-y}{r}=>x-y=r(CosA)__________(2)
 
Subtracting Equation (2) from (1)
 
y=r(Cos\frac{A}{2}-CosA)
Ans: \ The \ perpendicular \ distance \ between \ the \ two \ parallel \ chords \ is \ r(Cos\frac{A}{2}-CosA)
 

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