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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?

Sujit Kumar
111 Points
4 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)

$y=r(Cos\frac{A}{2}-CosA)$
$Ans: \ The \ perpendicular \ distance \ between \ the \ two \ parallel \ chords \ is \ r(Cos\frac{A}{2}-CosA)$