Question:
sir/maam good afternoon
my question is how to prove that 2 tangent drawn inside the circle is parallel if drawn straight through centre of circle like diameter.
Answer:
Let us suppose that l and m are the tangents to a circle such that l || m and intersecting at A and B.
Now a tangent at any point of a circle is perpendicular to the radius through the point of contact.
Then from the figure,
So ∠XAO = 90
and ∠YBO = 90
Since ∠XAO + ∠YBO = 90+90
=> ∠XAO + ∠YBO = 180
i.e angles on the same side of the transversal is 180.
So the line AB passes through the centre and is the diameter of the circle.
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