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O IS THE CENTRE OF A XIRCLE OF RADIUS 5CM.T IS A POINT SUCH THAT OT=13CM. AND OT INTERSECT THE CIRCLE AT E.IF AB IS THE TANGENT TO THE CIRCLE AT E,FIND LENGTH AB.

Asked by shabnakader 7th October 2017, 10:55 AM
Answered by Expert
Answer:
 
begin mathsize 16px style angle OPT equals 90 degree
In space triangle OPT comma space by space Pythagoras space theorem comma
OT squared equals OP squared plus PT squared
rightwards double arrow 13 squared equals 5 squared plus PT squared
rightwards double arrow PT equals 12 space cm
Since space lengths space of space tangents space drawn space from space straight a space point space to space straight a space circle space are space equal comma
AP equals AE equals straight x left parenthesis say right parenthesis
rightwards double arrow AT equals PT minus AP equals 12 minus straight x
Since space AB space is space straight a space tangent space to space he space circle space straight E. space
rightwards double arrow OE perpendicular AB
rightwards double arrow angle OEA equals 90 degree
rightwards double arrow angle AET equals 90 degree
rightwards double arrow AT squared equals AE squared plus ET squared
rightwards double arrow left parenthesis 12 minus straight x right parenthesis squared equals straight x squared plus left parenthesis 13 minus 5 right parenthesis squared
rightwards double arrow straight x equals 10 over 3 space cm
Similarly comma space BE equals 10 over 3 space cm
rightwards double arrow AB equals AE plus BE equals open parentheses 10 over 3 plus 10 over 3 close parentheses space cm equals 20 over 3 space cm end style
Answered by Expert 22nd December 2017, 9:36 AM
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