If the chord AB subtends an angle \alpha and chord CD subtends an angle \beta at the centre O, then what is the value of \tan(\frac{\beta}{2}) - \tan(\frac{\alpha}{2})?
Consider the following for the next two (02) items that follow : Two parallel chords AB and CD of a circle are of lengths 60 cm and 80 cm respectively. They are on the same side of the centre O and 10 cm apart.
- A. \frac{3}{4}
- B. \frac{5}{12}
- C. \frac{1}{2}
- D. \frac{7}{12} ✓
Correct Answer: D. \frac{7}{12}
Explanation
The perpendicular distance to AB is 40 cm, and its half-length is 30 cm, so \tan(\alpha/2) = \frac{30}{40} = \frac{3}{4}. The perpendicular distance to CD is 30 cm, and its half-length is 40 cm, so \tan(\beta/2) = \frac{40}{30} = \frac{4}{3}. Thus, \tan(\beta/2) - \tan(\alpha/2) = \frac{4}{3} - \frac{3}{4} = \frac{7}{12}.
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