AB is a chord of length 24cm of a circle of radius 13cm. The tangents at A and B intersect at C. Find the length AC.

 

Join Centre O with C and this line will be perpendicular bisector of AB.

Therefor AD=DB=12

OB=13

Therefor OD^2=(OB)^2-(DB)^2=25

Therefor OD=5

Let Angle ODB=X

In triangle ODB, tan X=DB/DO=12/5

In triangle OCB, tan X=CB/BO=CB/13

 

Equating both values of tan X

 

12/5=CB/13

Therefor CB=(12*13)/5=156/5=31.2