Homeclass 10MathsCirclesPoint Of Contact

Point Of Contact

The point of contact is the single, unique point where a tangent line touches a circle. It is the only point that the circle and the tangent line share in common.

Key Concepts

A tangent to a circle intersects the circle at exactly one point, which is known as the point of contact.
The radius of the circle drawn from the center to the point of contact is always perpendicular to the tangent line.
The shortest distance from the center of the circle to any point on the tangent line is the radius that meets the tangent at the point of contact.

Formula & Equation

Radius OP is perpendicular to Tangent AB at Point of Contact P (OP ⊥ AB).

O is the center of the circle, P is the point of contact, and AB is the tangent line.

Still confused about Point Of Contact?

Don't just read. Talk to our AI Teacher by voice, interrupt anytime, and clear your doubts instantly like a real classroom.

Download

Common Misconceptions

Myth: A tangent line touches the circle at two very close points or along a small curved segment.
Fact: A tangent line touches the circle at exactly one mathematical point, which is the point of contact. If a line touches or crosses the circle at two points, it is a secant, not a tangent.

Real World Applications

When a bicycle is parked on a flat road, the exact spot where the circular tire touches the flat ground represents the point of contact.
A circular coin standing upright on a flat table touches the surface at exactly one point of contact.

Frequently Asked Questions

How many points of contact can a single tangent have with a circle?
A single tangent line has exactly one point of contact with a circle.
What is the angle between the radius and the tangent at the point of contact?
The angle between the radius and the tangent at the point of contact is always 90 degrees, meaning they are perpendicular to each other.

Keep Learning

CircleTangentTangent-Radius Theorem