TANGENT
Definition Of Tangent
A tangent to a curve at a point is a straight line that touches the curve at that point.
Examples of Tangent
The line AB is a tangent to the circle at P.
A tangent line to a circle contains exactly one point of the circle
A tangent to a circle is at right angles to the radius of the circle at its point of contact
Video Examples: Tangents and Circles
Solved Example on Tangent
Ques: Find the number of tangents that can be drawn from a point inside a circle to the circle.
Choices:
A. 1
B. 2
C. infinite
D. 0
Correct Answer: D
Solution:
Step 1: No tangent can be drawn from a point inside a circle to it.
Quick Summary
- A tangent line touches a circle at exactly one point.
- A tangent to a circle is at right angles to the radius of the circle at its point of contact.
- No tangent can be drawn from a point inside a circle to the circle.
🍎 Teacher Insights
Use dynamic geometry software to demonstrate the relationship between the radius and tangent. Emphasize real-world applications such as wheels and axles.🎓 Prerequisites
- Circles
- Lines
- Angles
- Radius
- Diameter
Check Your Knowledge
Q1: How many tangents can be drawn from a point inside a circle to the circle?
Q2: A line touches a circle at one point. Is it always a tangent?
Frequently Asked Questions
Q: Can a tangent line intersect the circle at more than one point?
A: No, a tangent line intersects the circle at exactly one point.
Q: Is a tangent line always perpendicular to the radius at the point of tangency?
A: Yes, a tangent line is always perpendicular to the radius drawn to the point of tangency.
Q: How many tangents can be drawn from an external point to a circle?
A: Two tangents can be drawn from an external point to a circle, and these tangents are equal in length from the external point to the points of tangency.