Question

Can there be only one tangent from a particular point? Explain your answer.

Answer 1

Explanation:

If possible, Let PT and PT' be two tangents at a point P of the circle. Now, the tangent at any point of a circle is perpendicular to the radius through the point of contact.

This is possible only when PT and PT' coincide. Hence, there is one and only one tangent at any point on the circumference of a circle.

Answer 2

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Theorem. At any point on a circle's circumference, one and only one tangent can be drawn to it, and this tangent is perpendicular to the radius through the point of contact.

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If possible, Let PT and PT' be two tangents at a point P of the circle. Now, the tangent at any point of a circle is perpendicular to the radius through the point of contact. This is possible only when PT and PT' coincide. Hence, there is one and only one tangent at any point on the circumference of a circle.Theorem. At any point on a circle's circumference, one and only one tangent can be drawn to it, and this tangent is perpendicular to the radius through the point of contact.

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