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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