2018 · Q100
In the figure given below, two equal chords intersect at point P. If AB = CD = 10 cm, OC = 13 cm (O is the centre of the circle) and PB = 3 cm, then what is the length of OP?
Elementary MathematicsCircles
- A5 cm
- B6 cm
- C2√29 cm
- D2√37 cm
Explanation
For intersecting chords, AP × PB = CP × PD: 7 × 3 = 21 with CP + PD = 10, so {CP, PD} = {3, 7}. Placing P at the origin with AB on the x-axis puts the centre at (−2, ±12) (from |OA| = |OC| = 13), giving OP = √(4 + 144) = 2√37 cm, option (D).