Calculate the length of a chord which is at a distance 12 cm from the centre of a circle of radius 13 cm.

From figure,

AB is the chord which is at a distance 12 cm so,

OC = 12 cm and OA = radius = 13 cm.

In right angle triangle OAC,

⇒ OA² = OC² + AC² (By pythagoras theorem)

⇒ 13² = 12² + AC²

⇒ AC² = 13² - 12²

⇒ AC² = 169 - 144 = 25

⇒ AC = $\sqrt{25}$ = 5 cm.

Since, the perpendicular to a chord from the centre of the circle bisects the chord,

∴ CB = AC = 5 cm.

AB = AC + CB = 5 + 5 = 10 cm.

Hence, length of chord = 10 cm.