Question

Two concertric circles are of radii 6.5 cm and 2.5cm. Find the length of the chord of the larger circle which touches the smaller circle.

Answer 1

Let the two concentric circles with centre O.
AB be the chord of the larger circle which touches the smaller circle at point P.
∴ AB is tangent to the smaller circle to the point P.
⇒OP⊥AB
By Pythagoras theorem in Δ OPA,
$O{A}^2=A{P}^2+O{P}^2$
⇒${6.5}^2=A{P}^2+{2.5}^2$
⇒$A{P}^2=42.25-6.25$
⇒AP=6
In Δ OPB,
Since OP ⊥ AB,
AP = PB (∵ Perpendicular from the centre of the circle bisects the chord)
AB = 2AP = 2 × 6 = 12 cm
∴ The length of the chord of the larger circle is 12 cm.