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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?

rehab , 8 Years ago
Grade 11
anser 1 Answers
Sujit Kumar
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)
 
Last Activity: 8 Years ago
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