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?
Answer & explanation
Correct answer: option 3
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.