Question

In the figure XY and X'Y' are two parallel tangents to a circle with centre O and and another tangent AB with point of contact C interesting XY at A and X'Y' at B prove that .

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Solution
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Consider the problem
Let us join point to

In

(Radii of the same circle)
(Tangent from point )
(Common side)
( congruence criterion)

Therefore,


Similarly, 


Since, is a diameter of the circle, it is a straight line.

Therefore,

So, from equation and equation

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