2023 · Q36
If the chord AB subtends an angle α and chord CD subtends an angle β at the centre O, then what is the value of tan(β/2) − tan(α/2)?
Elementary MathematicsCircles
- A3/4
- B5/12
- C1/2
- D7/12
Explanation
Using the figure from Q35 (r=50): sin(alpha/2)=30/50=3/5 so tan(alpha/2)=3/4; sin(beta/2)=40/50=4/5 so tan(beta/2)=4/3. Difference=7/12. Option (d).