A chord AB of circle C₁, of radius 17 cm touches circle C₂, which is concentric to C₁. The radius of C₂ is 8 cm. What is the length (in cm) of AB?

30

According to the diagram

\( { AM}^{2 } \) = \( {OA }^{2 } \) - \( {OM }^{2 } \)

= \( { AM}^{2 } \) = \( {17 }^{2 } \) - \( {8 }^{2 } \)

= \( { AM}^{2 } \) = 289 - 64

= \( { AM}^{2 } \) = 225

= AM = 15 cm

Then, AB = 2 x AM

= AB = (2 x 15) cm

= AB = 30 cm

Therefore, AB is 30 cm.