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.

Asked by yashjain | 28th Nov, 2012, 04:13: PM

Expert Answer:

 
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

Answered by  | 29th Nov, 2012, 11:59: PM

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