In a circle with centre O, a tangent is drawn from an external point A to the circel which touches the circel at B. If OB = 5 cm, OA =13 cm, then the length of AB=

Options

A. 12 cm
B. 13 CM
C. `6.5 cm`
D. 6 cm

Explanation

In the circel with centre O, AB is a tangent and OB is a radius passing throgh point of contact.
`therefore OB bot AB, therefore angle OBA =90^(@)`
`therefore DeltaAOB` is a right-angaled triangle, of which OA is the hypotensius.
`therefore OB^(2) +AB^(2) =OA^(2)[by pythagoras' theorem]`
or `5^(2) +AB^(2) =13^(2) [because OB =5 cm, OA =13 cm]`
`or 25+AB^(2) =169or, AB^(2) =169 -25`
or `AB^(2) =144or, AB=sqrt144or, AB =12`
Hence the length of AB = 12 cm
`therefore ` (a) is correct.