A tangent to a circle is a line that is perpendicular to the radius at a particular point. The point where the radius and tangent are perpendicular to each other is known as the point of tangency. There are various conditions and precludes for the construction of tangents to a circle as mentioned below:
At a Particular Point of the Circle with Centre O:
Let’s take a circle with centre O and a point P on its circumference.
Hence, OP will be the radius of the circle.
Extend the radius OP further, outside the circle till M.
Now, adjust the compass in such a way, so that the opening of the compass is more than the radius OP.
Once the compass is adjusted accordingly, cut a semi-circle on OM while keeping the compass on O.
Similarly, cut a semi-circle by keeping the compass at M.
Now, join the semi-circles so formed to draw a tangent to a circle.
The point where OP and the perpendicular meet will be the point of tangency.
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At a Point Outside The Circle:
Let’s take a circle with centre O and point P outside the circle.
Q1. What do we Understand by the Tangent of a Circle?
Answer: A tangent circle is a line that begins from outside of the circle and bisects the plane of the circle at its periphery at precisely one point. The point where a tangent bisects the circle is what we call the point of tangency. Construction of Tangent is actually a standard concept of geometry.
Q2. What is a Tangent Generally?
Answer: A tangent in common can be any line, segment or a ray that can be a tangent to more than one circle simultaneously. There can be 1 to 4 numbers of common tangents to two circles. The point to be taken a note of is that a circle's tangent touches the circle but never really enters it. Moreover, multiple tangents to the 2 circles can be an inner tangent or an outer one to each other’s circles.
Q3. Is a Tangent Line to a Circle Perpendicular?
Answer: A tangent to a circle is a line that bisects the circle exactly at one point. This is the point that we call a point of tangency or tangency point. A substantial outcome is that the radius from the centre of the circle to the point of tangency is perpendicular to the tangent line.