Question

find the length of a tangent from the figure where O is the centre of the circle


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Answer 1

Answer:

by using Pythagoras theoram

(x-1)^2 + (x-3)^2 = ( x+1)^2

x^2 + 1 - 2x + x^2 + 9 - 6x = x^2 + 1 + 2x

x^2 + 9 - 6x- 4x = 0

x^2-10x+9 = 0

x = -b+ root of b^2-4ac/2a , -b-root of b^2-4ac/2a

x = 10+root of 100-36/2 , 10-root of 100-36/2

x = 10 + root of 64/2 , 10-root of 64/2

x = 10+8/2 , 10-8/2

x = 9,1

tangent length = x+1 = 10 or 2