PA is a tangent to a circle with center O and radius 6 cm form an external point p whose length is 8cm if B is a point on the circle such that P,O and B are collinear than find the length of PB.

Dear Student,

Please find below the solution to the asked query:

We form our diagram from given information , As :

Here , OA  =  OB  =   6  cm (  Given Radius is 6  cm )

And

PA  =   8  cm 

We know : The tangent intersects the circle's radius at a 90$°$ . So

We apply Pythagoras theorem In triangle POA and get

OP² = OA² + PA² , Substitute values we get

OP² = 6² + 8²

OP² = 36 + 64

OP² = 100

OP = 10 

And

OP  =  PB  +  OB  , So

10 =  PB  + 6 

PB  = 4 cm                                          ( Ans )


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