Question

O is the center of a circle of radius 5 cm. T is a point such that ot = 13 cm and ot intersects the circle at

e. If ab is a tangent to the circle at e, then find the length of ab.

Answer 1

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