In the given figure, O is the centre of a circle of radius 13 cm and AB is a chord perpendicular to OD. if CD = 8 cm, then what is the length (in cm) of AB?

Given : OB is the radius of circle = 13 cm and OC = OD - CD = $$13 - 8 = 5$$ cm

To find : AB = ?

Solution : The line from the centre of the circle to the chord bisects it at right angle.

=> AC = BC = $$\frac{1}{2}$$ AB

In $$\triangle$$ OBC,

=> $$(BC)^2=(OB)^2-(OC)^2$$

=> $$(BC)^2=(13)^2-(5)^2$$

=> $$(BC)^2=169-25=144$$

=> $$BC=\sqrt{144}=12$$ cm

$$\therefore$$ AB = $$2 \times$$ BC

= $$2 \times 12=24$$ cm

=> Ans - (C)