The radii of two concentric circles are 26 cm and 10 cm. If the chord of the greater circle is a tangent to the smaller circle, then find the length of that chord.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 48 cm
The radius from the circle's center to the tangency point is perpendicular to the tangent line.
Here, OC = 10 cm and OA = 26 cm
Also, ∠OCA = 90°
AB is the chord of the greater circle which is the tangent of the smaller circle.
Now, AC = √(OA2 - OC2) = √(262 - 102)
= √(676 - 100)
= √576
= 24 cm
AB = 2AC = 2(24) = 48 cm
Therefore, the length of the chord is 48 cm.