Tangents and Secants to a Circle
Telangana Board · Class 10 · Mathematics
Complete topic list for Tangents and Secants to a Circle in Telangana Board Class 10 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.
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Topics in Tangents and Secants to a Circle
Line and Circle Relationships
- Three possible positions of a line with respect to a circle: non-intersecting, secant (two intersection points), and tangent (one intersection point)
- A tangent touches the circle at exactly one point called the point of contact
- A secant intersects the circle at two distinct points, forming a chord between these points
Properties of Tangents
- Only one tangent can be drawn to a circle at any given point on the circle
- The tangent at any point of a circle is perpendicular to the radius through the point of contact
- From an external point, exactly two tangents can be drawn to a circle
Number of Tangents from Different Positions
- From a point inside the circle: No tangents possible
- From a point on the circle: Exactly one tangent
- From a point outside the circle: Exactly two tangents
Construction of Tangents
- To construct tangent at a given point on circle: Draw perpendicular to radius at that point
- To construct tangents from external point: Use circle with diameter as line joining external point to center
- The perpendicular bisector method is key for external point constructions
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