2019 · Q38
A line segment AB is the diameter of a circle with centre at O having radius 6.5 cm. Point P is in the plane of the circle such that AP = x and BP = y. In which one of the following cases does the point P not lie on the circle?
Elementary MathematicsCircles
- Ax = 6.5 cm and y = 6.5 cm
- Bx = 12 cm and y = 5 cm
- Cx = 5 cm and y = 12 cm
- Dx = 0 cm and y = 13 cm
Explanation
P lies on the circle iff angle APB is a right angle (Thales), i.e. x^2+y^2 = 13^2 = 169. Only option A fails: 6.5^2+6.5^2 = 84.5.