What happens when a line is tangent to a circle?

A tangent to a circle is a straight line which touches the circle at only one point. This point is called the point of tangency. The tangent to a circle is perpendicular to the radius at the point of tangency.

What does it mean when a triangle is tangent to a circle?

The tangent of an angle in a right triangle is a value found by dividing the length of the side opposite the given angle by the length of the side adjacent to the given angle. Tangent to a Circle Theorem. A line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency …

What is the point where the tangent touches the circle?

Point of tangency is the point where the tangent touches the circle. At the point of tangency, a tangent is perpendicular to the radius.

Is the point of contact of the circle and the tangent line?

point of tangency
A line that touches the circle at a single point is known as a tangent to a circle. The point where tangent meets the circle is called point of tangency. The tangent is perpendicular to the radius of the circle, with which it intersects.

Why is a tangent to a circle perpendicular to the radius?

The radius of a circle is perpendicular to the tangent line through its endpoint on the circle’s circumference. Conversely, the perpendicular to a radius through the same endpoint is a tangent line. The resulting geometrical figure of circle and tangent line has a reflection symmetry about the axis of the radius.

Why is a tangent of a circle is always perpendicular to the radius at the point of tangency?

The same will be the case for all other points on the tangent (l). So OA is shorter than any other line segment joining O to any point on l. Hence, the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Why is a tangent line perpendicular to the radius?

How do you prove that the tangent of a circle is perpendicular to the radius?

Tangent – Perpendicular to Radius

1. Given:
2. To prove: OP ⊥ XY.
3. Construction: On XY take any point Q, other than P.
4. Proof:
5. One and only one tangent can be drawn to a circle at a given point on the circumference because only one perpendicular can be drawn to Op through the point P.