If circular arcs $\widehat{A C}$ and $\widehat{B C}$ have centres at B (- $\alpha$ , 0) and A( $\alpha$ , 0) respectively and equation of circle which touches both arcs $\widehat{A C}$ and $\widehat{B C}$ and line AB is (x - a) 2 + (y - b) 2 = r 2 r > 0, if length of arc BC = 8 $\pi$ , the value of | $\alpha$ + b + r - $\alpha$ | equals:

Circles

Grade None

Question:

If circular arcs $\widehat{A C}$ and $\widehat{B C}$ have centres at B (-$\alpha$, 0) and A($\alpha$, 0) respectively and equation of circle which touches both arcs $\widehat{A C}$ and $\widehat{B C}$ and line AB is (x - a)2 + (y - b)2 = r2 r > 0, if length of arc BC = 8$\pi$, the value of |$\alpha$ + b + r - $\alpha$| equals:

5

3

2

6

Step-by-Step Solution

Key Concept: Utilize the internal tangency condition between circles (distance between centers equals the difference of radii) and the line-tangency condition ($r = |b|$) while leveraging symmetry to locate the center of the touching circle.

6

Correct Answer: D

Question:

Step-by-Step Solution

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