A circle is centered at point O with a radius of 10 cm. A perpendicular is drawn from O to a chord AB, and the length of this perpendicular is 6 cm. What is the length of the chord AB?

Q.A circle is centered at point O with a radius of 10 cm. A perpendicular is drawn from O to a chord AB, and the length of this perpendicular is 6 cm. What is the length of the chord AB?

Since a perpendicular drawn from the center of a circle to a chord bisects the chord, point D is the midpoint of chord AB. Given: OD = length of the perpendicular = 6 cm From the right-angled triangle ∆OBD, we get: \[ OD^2 + BD^2 = OB^2 \Rightarrow 6^2 + BD^2 = 10^2 \Rightarrow BD^2 = 100 - 36 = 64 \Rightarrow BD = \sqrt{64} = 8 \text{ cm} \] Therefore, \[ AB = 2 \times BD = 2 \times 8 = 16 \text{ cm} \] Hence, the length of chord AB is 16 cm.