2024 · Q39
The chord AB of a circle with centre at O is 2√3 times the height of the minor segment. If P is the area of the sector OAB and Q is the area of the minor segment of the circle, then what is the approximate value of P/Q ? (Take √3 = 1.7 and π = 3.14)
Elementary MathematicsCircles
- A1.4
- B1·7
- C2.2
- D2.6
Explanation
With AB = 2√3·h, Pythagoras on the half-chord gives the central angle 120°. Then P = (120/360)πr² and Q = P − (1/2)r²sin120°. Using √3 = 1.7 and π = 3.14, P/Q ≈ 1.7, option (b).