Question

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

Answer 1

We know that the radius and tangent are perpendicular at their point of contact In right triangle AOP

`AO^2 = OP^2 + PA^2`

⇒ `(6.5) ^2 = (2.5)^2 +PA^2`

⇒`PA^2 = 36`

⇒PA = 6cm

Since, the perpendicular drawn from the center bisects the chord.

∴ PA = PB = 6cm

Now , AB = AP + PB = 6+6 = 12cm

Hence, the length of the chord of the larger circle is 12cm.