10th Class Mathematics Solved Paper - Mathematics-2016 Outside Delhi Set-II

  • question_answer Prove that tangent drawn at any point of a circle is perpendicular to the radius through the point of contact.

    Answer:

    Given, a tangent AB at point P of the circle with centre O.
    To prove:           .
    Construction: Join OQ where Q is a point (other than P) on AB.
    Proof: Since Q is a point on the tangent AB (other than P).
     Q lies outside the circle.
    Let OQ intersect the circle at R.
    .
    But                   .         (Radii of the circle)
    .
    Thus, OP is the shortest distance than any other line segment joining O to any point of AB.
    But, we know that the shortest distance between a point and a line is the perpendicular distance
                         Hence Proved.


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