AB is a chord in a circle of radius 13 cm. From centre O, a perpendicular is drawn through AB intersecting AB at point C. The length of OC is 5 cm. What is the length of AB?
Answer & explanation
Correct answer: option 1
Radius OB = 13 cm,
AB is a chord, where a perpendicular line is intersecting AB at point C. OC = 5 cm
Calculation
Perpendicular drawn from the center of a circle to the chord bisects the chord.
AC = BC and angles OCB = \({90}^\circ\)
Thus, the triangle OCB is a right angled triangle.
Therefore, by Pythagoras Theorem
\( {OB }^{2 } \) = \( {OC }^{2 } \) + \( {CB }^{2 } \)
\( {CB }^{2 } \) = \( {OB }^{2 } \) - \( {OC }^{2 } \)
= \( {CB }^{2 } \) = \( {13 }^{2 } \) - \( {5 }^{2 } \)
= 169 - 25 = 144
CB = \(\sqrt {144 }\) = 12
AB = 2CB = 2 x 12 cm
Therefore, the length of AB is 24 cm.