Maths Class 10 Notes for Circles
The path of all points that are equidistant from a fixed point is called a circle.
SECANT OF A CIRCLE
A line which intersects a circle in two distinct points is called a secant of the circle.
NOTE : A line can meet a circle at most in two distinct points.
TANGENT TO A CIRCLE
A line which meets a circle exactly at one point is called a tangent to the circle. In adjoining figure, the line BAC is a tangent to the circle with centre O.
NOTE : The point where the line touches the circle is called its point of contact. In the figure ‘A’ is the point of contact.
1. All points other than the point of contact of a tangent to a circle lie outside the circle.
2. No tangent can be drawn to a circle through a point inside the circle.
3. Not more than one tangent can be drawn to a circle at a point on the circumference of the circle.
4. Two tangents can be drawn to a circle from a point outside the circle.
AB and AC are two tangents drawn from the point A to the circle with centre 0.
NOTE : The distance AB (or AC) is called the length of tangent.
THEOREMS RELATED TO TANGENT TO A CIRCLE
The tangent at any point of a circle is perpendicular to the radius through the point of contact. We have given a circle with centre 0 and a tangent XY to the circle at a point P then OP is perpendicular to XY.
The lengths of tangents drawn from an external point to a circle are equal. We have a circle with centre 0, a point P lying outside the circle and two tangents PQ, PR on the circle from P then PQ = PR.