2025 · Q65
In a circle of radius 14 cm, APB is the shorter arc and P is the midpoint of the arc. Let C be the midpoint of chord AB and PC=7 cm. What is the length of chord AP?
Elementary MathematicsCircles
- A3.5 cm
- B7 cm
- C10.5 cm
- D14 cm
Explanation
P, C, O are collinear (P is the arc midpoint), OP=14, PC=7, so OC=7. In triangle OCA: AC=sqrt(14^2-7^2)=7*sqrt(3). Then AP=sqrt(PC^2+AC^2)=sqrt(49+147)=14. Assuming C=O (i.e. PC=radius) is the trap - PC is only half the radius.