2016 · Q48
In a circle of radius 3 units, a diameter AB intersects a chord of length 2 units perpendicularly at P. If AP > BP, then what is the ratio of AP to BP? (Express as (3 + 2√2) : (3 − 2√2))
Elementary MathematicsCircles
- A3 + 10 : 3 - 10
- B3 + 8 : 3 - 8
- C3 + 3 : 3 - 3
- D3 + 3
Explanation
Note: the options are garbled ('3 + 8' = 3+√8 = 3+2√2). The half-chord is 1, so OP = √(9−1) = 2√2. With AP>BP we get AP = 3+2√2 and BP = 3−2√2, a ratio of (3+2√2):(3−2√2) (option B).