A circle has important elements such as chords, secants, and tangents. Go through the given video to understand these concepts.
The theorem about tangents states that:
A tangent at any point of a circle is perpendicular to the radius through the point of contact.
In the above figure O is the centre of circle, line l is the tangent and P is point of contact.
∴ l ⊥ OP
It is given that O is the centre of the circle, l is the tangent to this circle and P is the point of contact.
Let us assume l is not perpendicular to the radius of the circle.
In this case, let us draw perpendicular OA to tangent l. Thus, point A is distinct from point P.
Let B be any point on tangent such that BAP is a line and BA = AP.
Now, in ΔOAB and ΔOAP, we have
OA = OA (Common side)
∠OAB = ∠OAP (OA ⊥ tangent l)
BA = AP (By construction)
∴ OB = OP (By CPCT)
Since OB = OP, point B also lies on the circle.
Also, point B is different from point P.
Thus, tangent l touches the circle at two distinct points. This contradicts the ...
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