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

AO² = OP² + PA²

\(\Rightarrow\) (6.5)² = (2.5)² + PA²

\(\Rightarrow\) PA² = 36

\(\Rightarrow\) PA = 6cm

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

∴ PA = PB = 6cm

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

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