Practicing Success
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? |
24 cm 12 cm 20 cm 15 cm |
24 cm |
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. |