Circles are inscribed in the acute angle α so that every neighbouring circles touch each other. If the radius of the first circle is R, then find the sum of the radii of the first n circles in terms of R and α .
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Radius of first circle = R
Let Radius of second circle be = R ′
= cosec 
∴ OB = R cosec 
Now 
= cosec 
⇒ OB ′ = R ′ cosec 
= OB + R + R ′
⇒ R + R cosec 
+ R ′ = R ′ cosec 
⇒ R(1 + cosec α /2) = R ′ (cosec α /2 – 1)
⇒ R ′ = R 
if radius of the third circle be R ′′ , then similarly R ′′ = R 
So R + R ′ + R ′′ + .....n terms = R 
= R 
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