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why we draw tangent line to any point on the circle?

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In Engineering, while drawing velocity diagrams for various mechanisms, we require the instantaneous radial and instantaneous tangential velocities. The direction of the second quantity, as the name implies, is in the direction of the tangent to the circle or curve at that point.
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Math Educator for Std.11th ,12th , Engineering Entrance and Degree Level with 11+ Years Experience

As it passes through the point where the tangent line and the curve meet, called ... method of drawing tangents, by considering a curve as described by a moving point ... Further developments we due to John Wallis, Isaac Barrow until the full ... Circles, parabolas, hyperbolas and ellipses do not have...
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As it passes through the point where the tangent line and the curve meet, called ... method of drawing tangents, by considering a curve as described by a moving point ... Further developments we due to John Wallis, Isaac Barrow until the full ... Circles, parabolas, hyperbolas and ellipses do not have any inflection point. read less
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join line given point with center and tangent line is perpendecular to that line passing through given point
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In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Roughly speaking, it is a line through a pair of infinitely close points on the circle. Tangent lines to circles form the subject of several theorems,...
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In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Roughly speaking, it is a line through a pair of infinitely close points on the circle. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs. Since the tangent line to a circle at a point P is perpendicular to the radius to that point, theorems involving tangent lines often involve radial lines and orthogonal circles. read less
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